Chinese Currency Exchange Rates Forecasting with EMD-Based...

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Research Article Chinese Currency Exchange Rates Forecasting with EMD-Based Neural Network Jying-Nan Wang , 1,2 Jiangze Du , 3,4 Chonghui Jiang , 3,4 and Kin-Keung Lai 5 1 College of International Finance and Trade, Zhejiang Yuexiu University of Foreign Languages, Shaoxing, Zhejiang, China 2 Research Institute for Modern Economics and Management, Zhejiang Yuexiu University of Foreign Languages, Shaoxing, Zhejiang, China 3 School of Finance, Jiangxi University of Finance and Economics, Nanchang, China 4 Research Centre of Financial Management and Risk Prevention, Jiangxi University of Finance and Economics, Nanchang, China 5 Department of Industrial and Manufacturing Systems Engineering, e University of Hong Kong, Pok Fu Lam, Hong Kong Correspondence should be addressed to Jiangze Du; [email protected] Received 27 June 2019; Revised 1 September 2019; Accepted 19 September 2019; Published 30 October 2019 Guest Editor: Benjamin M. Tabak Copyright © 2019 Jying-Nan Wang et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e Chinese currency, RMB, is developing as an international currency. erefore, the effective strategy for trading RMB exchange rates would be attractive to international investors and policymakers. In this paper, we have constructed hybrid EMD-MLP models to forecast RMB exchange rates and developed a trading strategy based on these models. Empirical results show that the proposed hybrid EMD-MLP * model always performs best based on both NMSE and D stat criteria when the forecasting period is greater than five days. Moreover, we compare the models’ performance using different horizons and find that accuracy will increase with the growth of the forecasting horizons; however, the NMSE will become larger. Lastly, we adopt the best performing model to develop trading strategies with longer forecasting horizons when considering the number of profitable trading activities. If we consider a 0.3% transaction cost, the developed strategy will bring an annual return exceeding 10%, as well as enough trading opportunities. 1. Introduction As the Chinese government continues the process of RMB internationalization, RMB currency trading becomes in- creasingly important in personal investment, corporate financial decision-making, governments’ economic poli- cies, and international trade and commerce. e RMB has therefore attracted an increasing attention from policy- makers, investment institutions, and entrepreneurs worldwide. One reflection of this is the 2015 finding of the Society for Worldwide Interbank Financial Telecommu- nication (SWIFT) that the RMB has overtaken the Japanese yen to become the fourth ranking world payment currency. e first milestone in the process of RMB in- ternationalization is the establishment of an RMB offshore center in Hong Kong in 2004. In December 2008, the Chinese Premier announced the pilot program for cross border trade settlement in RMB, making the offshore RMB officially deliverable in Hong Kong. From July 19, 2010, the offshore market for RMB officially commenced. Recent literature [1–4] has found that RMB movements have an impact on regional currencies. Due to the importance of the RMB, the purpose of this study is to create a reliable RMB forecasting model and provide a possible application for designing trading strat- egies. Two kinds of current rates for exchanging the US dollar (USD) into Chinese RMB will be considered. If the RMB is traded onshore (in mainland China), it is referred to as CNY, whereas if traded offshore (mainly in Hong Kong), it is designated as CNH. Since the onshore and offshore markets might respond differently to changes depending on financial markets, the CNY and CNH are not always at the Hindawi Complexity Volume 2019, Article ID 7458961, 15 pages https://doi.org/10.1155/2019/7458961

Transcript of Chinese Currency Exchange Rates Forecasting with EMD-Based...

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Research ArticleChinese Currency Exchange Rates Forecasting with EMD-BasedNeural Network

Jying-Nan Wang 12 Jiangze Du 34 Chonghui Jiang 34 and Kin-Keung Lai 5

1College of International Finance and Trade Zhejiang Yuexiu University of Foreign Languages Shaoxing Zhejiang China2Research Institute for Modern Economics and Management Zhejiang Yuexiu University of Foreign Languages ShaoxingZhejiang China3School of Finance Jiangxi University of Finance and Economics Nanchang China4Research Centre of Financial Management and Risk Prevention Jiangxi University of Finance and Economics Nanchang China5Department of Industrial and Manufacturing Systems Engineering e University of Hong Kong Pok Fu Lam Hong Kong

Correspondence should be addressed to Jiangze Du jiangzeduhotmailcom

Received 27 June 2019 Revised 1 September 2019 Accepted 19 September 2019 Published 30 October 2019

Guest Editor Benjamin M Tabak

Copyright copy 2019 Jying-Nan Wang et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

e Chinese currency RMB is developing as an international currencyerefore the eective strategy for trading RMB exchangerates would be attractive to international investors and policymakers In this paper we have constructed hybrid EMD-MLPmodels to forecast RMB exchange rates and developed a trading strategy based on these models Empirical results show that theproposed hybrid EMD-MLPlowast model always performs best based on both NMSE and Dstat criteria when the forecasting period isgreater than ve days Moreover we compare the modelsrsquo performance using dierent horizons and nd that accuracy willincrease with the growth of the forecasting horizons however the NMSE will become larger Lastly we adopt the best performingmodel to develop trading strategies with longer forecasting horizons when considering the number of protable trading activitiesIf we consider a 03 transaction cost the developed strategy will bring an annual return exceeding 10 as well as enoughtrading opportunities

1 Introduction

As the Chinese government continues the process of RMBinternationalization RMB currency trading becomes in-creasingly important in personal investment corporatenancial decision-making governmentsrsquo economic poli-cies and international trade and commerce e RMB hastherefore attracted an increasing attention from policy-makers investment institutions and entrepreneursworldwide One reection of this is the 2015 nding of theSociety for Worldwide Interbank Financial Telecommu-nication (SWIFT) that the RMB has overtaken the Japaneseyen to become the fourth ranking world payment currencye rst milestone in the process of RMB in-ternationalization is the establishment of an RMB oshorecenter in Hong Kong in 2004 In December 2008 the

Chinese Premier announced the pilot program for crossborder trade settlement in RMB making the oshore RMBopoundcially deliverable in Hong Kong From July 19 2010 theoshore market for RMB opoundcially commenced Recentliterature [1ndash4] has found that RMB movements have animpact on regional currencies

Due to the importance of the RMB the purpose of thisstudy is to create a reliable RMB forecasting model andprovide a possible application for designing trading strat-egies Two kinds of current rates for exchanging the USdollar (USD) into Chinese RMB will be considered If theRMB is traded onshore (in mainland China) it is referred toas CNY whereas if traded oshore (mainly in Hong Kong)it is designated as CNH Since the onshore and oshoremarkets might respond dierently to changes depending onnancial markets the CNY and CNH are not always at the

HindawiComplexityVolume 2019 Article ID 7458961 15 pageshttpsdoiorg10115520197458961

same price level Craig et al [5] and Funke et al [6] studyCNY-CNH pricing differentials in detail

It is well documented that the exchange rate series isconsidered as nonlinear and nonstationary time series andinteractively influenced by many factors which makes theaccurate forecasting of exchange rate rather challengingDuring past decades traditional econometric and statisticaltechniques including autoregressive integrated movingaverage (ARIMA) cointegration analysis vector autore-gression (VAR) and error correction (ECM) models havebeen widely used in foreign exchange rates forecastingHowever in the real-world financial markets exchange rateseries are nonlinear and rarely form purely linear combi-nations [7ndash10] us the above traditional models alwaysprovide unreliable forecasting if one continue applying thesetraditional econometric and statistical models e mainreason of this deficiency is that traditional econometric andstatistical models are constructed based on linear assump-tions which will be unable to capture the nonlinear featureshidden in the exchange rate series

Considering the limitation of traditional econometricand statistical models many nonlinear artificial intelligencemodels (AI) such as artificial neural networks (ANN)[11 12] feedforward neural networks (FNN) [13 14]support vector regression (SVR) [15ndash17] and genetic pro-gramming (GP) [18 19] have been applied to investigate theforecasting ability of financial time series Yu et al [20]provide a complete review of foreign exchange rate fore-casting with ANN and also introduce SVR and GP How-ever many AI-based models also have their ownshortcomings For instances ANN usually suffers fromoverfitting and local minima while other models includingGP and SVR are sensitive to parameter estimation Recentlydue to the complex characteristics of exchange rate seriesseveral studies show that a single model is unable to captureall the features and make accurate forecasts [21]

To overcome above shortcomings many researchersstart to rely on the hybrid model to forecast exchange rateseries accurately e composite forecasting method allowsus to obtain an approach to the dynamics underlying thedata by combining the predictions obtained from differentindividual techniques Alvarez-Dıaz and Alvarez [22] at-tempt to exploit the nonlinear structure by constructing thegenetic programming and neural networks compositemethod and apply this composite method to forecast YenUS$ and Pound SterlingUS$ exchange rates Other scholarsalso try to improve the forecasting accuracy of exchange rateseries by applying hybrid forecasting models For exampleZhao and Yang [23] andWong et al [24] use fuzzy clusteringand ANN to forecast financial time series Yu et al [25]propose an online big data-driven oil consumption fore-casting model based on Google trend by combining therelationship investigation and prediction improvement Yuet al [14] design a novel ensemble forecasting approach forcomplex time series by coupling sparse representation (SR)and feedforward neural network (FNN) ie the SR-basedFNN approach

e empirical mode decomposition (EMD) technique isfirst proposed by Huang et al [26] From the theoretical

views EMD is suitable for time series data in terms ofdecomposing the original data into components whichcould break the forecasting task down into simpler fore-casting subtasks ese decompositions consist of a finiteand often small number of intrinsic mode functions (IMFs)and one residual From the perspective of financial practicevarious economic activities may cause a different impactperiodicity on the exchange rate for example the companyrsquosfinancial report is released quarterly but government eco-nomic indicators are usually published once a year EMD ispotentially helpful in decomposing these effects and leads toimprove forecasting works ere are several studiesemploying the EMD technique in hybrid models For in-stance Yu et al [27] forecast crude oil prices with an EMD-based neural network model Chen et al [28] also combineEMD and the ANN approach to forecast tourism demandand Lin et al [29] propose a hybrid model using EMD andSVR for foreign exchange rate forecasting In this empiricalexperiment the original CNY or CNH price series withcharacteristics of nonlinearity and nonstationarity are di-vided into several independent subseries by the EMDtechnique and then partial or all IMFs and one residual areused to forecast Tang et al [30] combine the ensembleempirical mode decomposition (EEMD) with randomvector functional link (RVFL) network and find the pro-posed EEMD-based RVFL network performs significantlybetter in terms of prediction accuracy than not only singlealgorithms such as RVFL network extreme learning ma-chine (ELM) kernel ridge regression random forestbackpropagation neural network least square support vectorregression and autoregressive integrated moving averagebut also their respective EEMD-based ensemble variantsWesummarize in Table 1 the main characteristics of thesestudies on individual and hybrid forecasting methods in therecent literature

is study will focus on using ANN to forecast the RMBwith different forecasting horizons of 1 5 10 20 and 30days Nevertheless Huang et al [32] show that ANN per-forms better than the random walk while the forecastinghorizon is less than five days but for longer horizons such as10 and 30 days the general performance of ANN is worsethan the random walk model In this study a type offeedforward artificial neural network model called multi-layer perceptron (MLP) is adopted Empirical studies consistnot only of the pure MLP model but also a hybrid modelwith EMD to improve forecasting performance

In this study the hybrid forecasting model combiningMLP and EMD is similar to the work of Yu et al [27]However this study further considers the influence of IMFsthat have different levels of frequency In concrete termshigher frequency IMFs could be regarded as noise com-ponents when our forecasting horizon is longer Based onthis concept two hybrid models are proposed and namedEMD-MLP and EMD-MLPlowast Comparing these to pureMLP the former adjusts the original time series data bysubtracting higher frequency IMFs and then uses MLP tocompute the one-day ahead predictions e EMD-MLPlowastmodel applies the ldquodivide-and-conquerrdquo principle to con-struct a novel forecasting methodology in which partial or

2 Complexity

all IMFs and one residual are used According to the em-pirical evidence in this study both types of hybrid modelsare superior to the pureMLPmodel whether with 1- 5- 10-20- or 30-day forecasting horizons Moreover the appli-cation of trading strategies is proposed Although thetransaction costs can make the profits practically disappearor become negative as proved by Alvarez Dıaz [31] thisempirical analysis shows that even considering a 03transaction cost in each trade the trading strategy based onEMD-MLP on average produces an annualized profit ex-ceeding 10

In this paper we will investigate RMB exchange rateforecasting and develop the relevant trading strategies basedon the constructed models e main contributions come

from three aspects First this study focuses on the RMBincluding the onshore RMB exchange rate (CNY) and off-shore RMB exchange rate (CNH) We will use daily data toforecast RMB exchange rates with different horizons basedon three types of models ie MLP EMD-MLP and EMD-MLPlowast Second we will consider not only theMLPmodel butalso the hybrid EMD-MLP and EMD-MLPlowast models toimprove forecasting performance It should be noted thatthe EMD-MLPlowast is different from the methodology proposedby Yu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBFinally we will choose the best forecasting models toconstruct the trading strategies by introducing differentcritical numbers and considering different transaction costs

Table 1 Literature on individual and hybrid forecasting models

Study Type Algorithm Data Timerange Criteria

Aladag et al [11] Individual ANN Exchange rates (TLEUR LEUEUR) 2005ndash2012 RMSE

Alvarez-Diaz andAlvarez [18] Individual GP Exchange rates (various pairs) 1971ndash2000 R-square

Alvarez-Dıaz andAlvarez [22] Individual GP ANN Exchange rates (GBPUSD JPY

USD) 1973ndash2002 NMSE SR

Alvarez Dıaz [31] Individual GP Exchange rates (GBPUSD JPYUSD) 1973ndash2002 U-eil value SR

Huang et al [32] Individual ANN Exchange rates (USDGBP USDJPY) 1997ndash2002 RMSE

Kajitani et al [13] Individual ANN Canadian lynx data 1821ndash1934 RMSENeely et al [19] Individual GP Exchange rates (various pairs) 1974ndash1995 Excess returnNikolsko-Rzhevskyy andProdan [33] Individual Markov switching Exchange rates (various pairs) 1983ndash2008 MSE

Wong et al [24] Individual Novel ANN Simulated time series data ndash MAPE NMSEYu et al [16] Individual Least squares SVM Crude oil 2008ndash2015 MAPE

Yu et al [25] Individual Artificial intelligence Global oil consumption 2004ndash2015 PCC AUC RMSEMAPE

Zhang [10] Individual ANN Simulated time series data mdash MSE MAPE

Zhao and Yang [23] Individual CRPSO-based neuronmodel

Simulated time series dataelectroencephalogram data mdash MSE

Cao [15] Hybrid SVM+SOMSunspot data Santa Fe datasets AC and D and the two building

datasetsmdash NMSE RMSE CV

Chen et al [28] Hybrid EMD+ANN Tourism demand 1971ndash2009 MAPE RMSE MAE

Khashei et al [7] Hybrid ARIMA+ANNs+ fuzzy Exchange rates (USDIran rials)gold price 2005ndash2006 MAE MSE

Lin et al [29] Hybrid EMD+SVM Exchange rates (various pairs) 2005ndash2009 MAPE RMSE MAEDS CP CD

Tang et al [30] Hybrid EEMD+RVFL Crude oil 1986ndash2010 MAPE RMSE DSYu et al [12] Hybrid ANN+WD Patient visits 2010ndash2015 RMSE MAPEYu et al [27] Hybrid EMD+ANN Crude oil 1986ndash2006 NMSE DS

Yu et al [17] Hybrid OPL+ SVMQR Ten publicly available datasets mdash Empirical riskquantile property

Yu et al [14] Hybrid Sparserepresentation +ANN Crude oil 1986ndash2013 RMSE MAPE

Zhang [21] Hybrid ARIMA+ANN Wolfrsquos sunspot data Canadian lynxdata and GBPUSD mdash MSE MAE

ANN artificial neural network SVM support vector machine GP genetic programming CRPSO cooperative random learning particle swarm optimizationRVFL random vector functional link OPL orthogonal pinball loss SVMQR SVM quantile regression WD wavelet decomposition SOM self-organizationfeature map RMSE root mean squared error NMSE normalized mean squared error MAE mean absolute error MAPE mean absolute percentage errorCV coefficient of variation PCC percentage correctly classified accuracy AUC area under the receiver operating curve SR success ratio DS directionalsymmetry CP correct uptrend CD correct downtrend

Complexity 3

e remainder of the paper is organized in the followingmanner Section 2 provides a brief description of ANN andEMD e overall forecasting process and model notationsof three kinds of forecasting models are also included in thispart In Section 3 two currency exchange rates of USD toRMB CNY and CNH are used to test the effectiveness ofthe proposed methodology and the selected models areapplied in trading strategies e conclusions drawn fromthis study are presented in Section 4

2 Methodology

21 Artificial Neural Network (ANN) is study considersMLP based on an error backpropagation algorithm Figure 1shows a simple MLP structure with three input nodes (X1X2 and X3) One hidden layer consists of four hidden nodesand one output node (Y) e nodes are organized in layersand are usually fully connected by weights which indicatethe effects of the corresponding nodes In each node of thehidden and output layers all data are firstly processed by theintegration function (also called the summation function)which combines all incoming signals and secondly pro-cessed by the activation function (also called the transferfunction) which transforms the output of the node Ingeneral the amount of the hidden layer is less than 3 due tothe converging restriction

Particularly the MLPmodel is fitted by the training dataand then the testing data and an out-of-sample dataset areused to verify its forecasting performance rough super-vised learning algorithms the parameters (weights and nodeintercepts) are adjusted iteratively by a process of mini-mizing the forecasting error function Formally an MLPwith an input layer with n nodes one hidden layer consistingof J hidden nodes and an output layer with one output nodecalculates the following function

o(x) f w0 + 1113944

J

j1wj middot f w0j + 1113944

n

i1wijxi

⎛⎝ ⎞⎠⎛⎝ ⎞⎠

f w0 + 1113944

J

j1wj middot f w0j + wT

j x1113872 1113873⎛⎝ ⎞⎠

(1)

where x (x1 xn) is the vector of all input variables w0is the intercept of the output node w0j is the intercept of thejth hidden node wj denotes the weight corresponding to thenode starting at the jth hidden node to the output node andwij denotes the weight corresponding to the node starting atith input node to the jth hidden node erefore all hiddenand output nodes calculate the function f(g(z)) where g(middot)

denotes the integration function which is defined asg(z) w0 + wtz and f(middot) denotes the activation functionwhich is often a bounded nondecreasing nonlinear anddifferentiable function In this study the logistic function(f(u) 1(1 + eminus u)) is used as the activation function

Given inputs x and the current weights which areinitialized with random values from a standard normaldistribution the MLP produces an output o(x) en anerror function is defined is study selects the mean squareerror as follows

E 1N

1113944

N

h1oh(x) minus yh( 1113857

2 (2)

where N is the number of data samples and yh is the ob-served output During the iterative training process theabove steps are repeated to adapt all weights until a pre-specified criterion is fulfilled In order to find a local min-imum of the error function the resilient backpropagationalgorithm modifies the weights in the opposite direction ofpartial derivatives According to Riedmiller and Braun [34]the weights are adjusted by the following rule

w(t+1)k w

tk minus η(t)

k middot signzE(t)

zw(t)k

⎛⎝ ⎞⎠ (3)

where t and k index the iteration steps and the weightsrespectively In order to speed up convergence the learningrate η(t)

k increases if the corresponding partial derivativekeeps the same sign otherwise it will decrease

22 EmpiricalModeDecomposition (EMD) In this study wefurther apply EMD to decompose the time series into severalIMFs and remaining residuesese IMFs usually satisfy twoconditions the first is that the number of extrema and zerocrossings must be equal or different by not more than oneSecond the mean value of the envelopes which include bothlocal maxima and minima must be zero at all points

Given the time series data x(t) t 1 2 T Huanget al [26] propose a sifting process to decompose x(t) efirst step is to identify all local maxima and local minima ofx(t) en the upper and lower envelopes are defined byconnecting all local extrema by a spline line Next for allpoints at the envelope the mean value m1

1(t) from upper andlower envelopes is calculated en it follows computationof the first IMF of x(t)

X1

H11

H12

H13

X3

Y

H14

X2

1 1

Input layer Hidden layer Output layer

w1j

w0j

w0

w2j

w3j

w1

w2

w3

w4

Figure 1 An artificial neural network structure with three inputneurons (X1 X2 and X3) one hidden layer consisting of fourhidden neurons (H11 H12 H13 and H14) and one output neuron(Y)

4 Complexity

h11(t) x(t) minus m

11(t) (4)

If h11(t) does not meet the above two conditions this

study then takes h11(t) as a new data series and repeats

procedure (4) us we calculate

h12(t) h

11(t) minus m

12(t) (5)

In this calculation m12(t) is the mean value of the upper

and lower envelopes of h11(t)

Repeating the same procedure until meeting bothconditions we get the first IMF component of x(t) c1(t)that is

c1(t) h1q(t) (6)

e stopping rule indicates that absolute values of theenvelope meanmust be less than the user-specified tolerancelevel In this study the tolerance level is denoted as thestandard deviation of x(t) times 001 Other interestingstopping rules can be found in the works of Huang et al [26]and Huang and Wu [35]

After extracting the component c1(t) from x(t) wedenote another series r1(t) x(t) minus c1(t) which containsall information except c1(t) Huang et al [36] suggest asifting stop criterion that is rn(t) becomes a monotonicfunction or cannot extract more IMFs Finally the timeseries x(t) can be expressed as

x(t) 1113944n

i1ci(t) + rn(t) (7)

where n is the number of IMFs and rn(t) is the final residuewhich represents the central tendency of the data series x(t)ese IMFs are nearly orthogonal to each other and all havemeans of nearly zero According to the above properties it ispossible to forecast all decompositions and summarize theseestimations to predict x(t)

23 Overall Forecasting Process and Model NotationsConsidering the time series pt t 1 2 T we would liketo predict l-day ahead which is denoted as 1113954pt+l In this studythe input variables (past observations) include ptminus 59 ptminus 19ptminus 9 and ptminus 4 to pt which represent the past price levels of60 days 20 days 10 days and the last 5 days respectivelye output is the l-day ahead prediction Formally it couldbe shown as follows

1113954pt+l φ pt ptminus 4 ptminus 9 ptminus 19 ptminus 59w( 1113857 (8)

where φ(middot) is a function determined by neural networktraining and w is a weight vector of all parameters of MLP

ree kinds of forecasting models are adopted in thisstudy e first is the pure MLP model with one and twohidden layers e second is an EMD-MLP model whichuses EMD to subtract some volatile IMFs from the originaldata series and then uses the new data series to calculate thefinal prediction by MLP technology Figure 2 indicates theprocedure of the EMD(-1)-MLP model which means thefirst IMF component is ignored e third kind of model is

named EMD-MLPlowast which generally consists of the fol-lowing four steps

(1) Decompose the original time series into IMF com-ponents and one residual component via EMD

(2) Determine how many IMF components are usedwhich depends on the length of the forecastingperiod

(3) For each chosen IMF and residual component theMLP model is used as a forecasting tool to modelthese components and to make the correspondingprediction

(4) Add all prediction results to one value which can beseen as the final prediction result for the original timeseries

As an example Figure 3 represents the above procedureof the EMD(-1)-MLPlowast model Time series data aredecomposed via EMD and generates n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) In addition toc1(t) we forecast each decomposition and then sum them asthe prediction results for the original time series

3 Empirical Experiments

31 Data Two kinds of currency exchange rates of USD toRMB are considered in this study If the RMB is tradedonshore (in mainland China) it is referred to as CNY and iftraded offshore (mainly in Hong Kong) it is named CNH

MLP

Prediction

hellip

Time series data

EMD

New series data

c1(t) c2(t) cn(t) rn(t)

sum

Figure 2 An example of the EMD(-1)-MLPmodelWe decomposea time series data by the EMD and generate n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) We sum all de-compositions except c1(t) to produce a new time series data enthe MLP is applied to compute the prediction

Complexity 5

Both time series data are downloaded from Bloomberg ForCNY daily data from January 2 2006 to December 21 2015with a total of 2584 observations are examined in this studySince the CNH officially commenced on July 19 2010 itssample period is from January 3 2011 to December 21 2015with a total of 1304 observations For training the neuralnetwork models two-thirds of the observations are ran-domly assigned to the training dataset and the remainder isused as the testing dataset In addition it should be notedthat the time series in price levels is used in the followinganalysis rather than in return levels

According to descriptions shown in Section 32 theEMD technique is used to decompose both CNY and CNHprice series into several independent IMFs and one residualcomponent e decomposed results of CNY and CNH arerepresented in Figures 4 and 5 Comparing these two figuresthe original data series and decompositions seem dissimilarwhich is due to the different lengths of the sample periods Infact their IMFs have some similar characteristics Firstfocusing on the sample period 2011ndash2015 their residualcomponents have the same trend Starting at about 65 theydrop slightly to 62 and then rise slightly to 65 Second theswing period of high-frequency IMFs is shorter and also themean of absolute values of high-frequency IMFs is smallerwhen compared with low frequency For example in theseries of CNY the absolute values of c1 c3 and c5 are000298 000596 and 002002 respectively In our estima-tion model it is not necessary to include all the high-fre-quency IMFs as considering high-frequency IMFs may

reduce the forecasting accuracy when the forecasting periodis long erefore in the model EMD-MLP the high-fre-quency IMF is removed to get the denoised time series Inthe model EMD-MLPlowast not only are all the decompositionschosen to forecast the exchange rate but consideration isalso given to using part of the decompositions to conductforecasting discarding the high-frequency IMF series

32 Experimental Results Two main criteria are consideredin this empirical experiment the normalized mean squarederror (NMSE) and the directional statistic (Dstat) to eval-uate the levels of prediction and directional forecastingrespectively Typically following [37] the NMSE is definedby

NMSE 1σ2Ψ

1Nt

1113944sisinΨ

1113954ps+l minus ps+l( 11138572 (9)

where Ψ refers to the test dataset containing Nt observa-tions 1113954ps+l is the l-day ahead prediction ps+l is the actualvalue and σ2Ψ is the variance of ps+l Clearly the NMSE isone of the most important criteria for measuring the validityof the forecasting model but from a business perspectiveimproving the accuracy of directional predictions cansupport decision-making so as to generate greater profitsFurthermore the Diebold-Mariano (DM) test [38] isadopted to investigate whether adding EMD could improvethe forecasting performance of the MLP model Specificallythe null hypothesis is that the EMD-MLP (or EMD-MLPlowast)model has a lower forecast accuracy than the correspondingMLP model For example in the case of the EMD(-1)-MLP(53) the corresponding model infers the MLP(53)model

Besides the NMSE evaluation the directional statistic(Dstat) is applied to measure the ability to predict movementdirection [27 39] which can be expressed as

Dstat 1

Nt

1113944sisinΨ

as times 100 (10)

where as 1 if (1113954ps+l minus ps)(ps+l minus ps)ge 0 and as 0 other-wise Pesaran and Timmermann [40] provide the directionalaccuracy (DAC) test to examine predictive performance Inthis case the DAC test is used to determine whether Dstat issignificantly larger than 05 We have also adopted the excessprofitability test proposed by Anatolyev and Gerko [41] inevery related empirical study Since both tests produce thesame outcome we only report the results of DAC tests in thefollowing empirical studies

Table 2 compares the forecasting performance in termsof the NMSE for the MLP EMD-MLP and EMD-MLPlowastmodels e NMSE is reported as the percentage for l-dayahead predictions where l 1 5 10 20 and 30 For eachprediction period the minimumNMSE is designated in boldfont Panel A of Table 2 displays the experimental results ofthe MLP models It is clear that with the increase inforecasting period the NMSE becomes larger suggestingreduced forecasting accuracy for a longer forecasting periodAlso the more complex MLPmodels with two hidden layers

MLP

Prediction

MLP MLPhellip

Time series data

EMD

c1(t) c2(t)

c2(t)

cn(t)

cn(t)

sum

rn(t)

rn(t)ˆ ˆ ˆ

Figure 3 An example of the EMD(-1)-MLPlowast model We de-compose a time series data by the EMD and generate n IMFcomponents c1(t) c2(t) cn(t) and one residue rn(t) Besidesc1(t) we forecast each decomposition and them sum them as theprediction

6 Complexity

do not offer better forecasting accuracy and are even worsefor 1-day ahead prediction

e empirical results of EMD-MLP are discussed inPanel B of Table 2 EMD(-1)-MLP treats the highest fre-quency IMF c1 as noise and applies the MLP model aftersubtracting the c1 series from the original time seriesEmpirical results show that the NMSE of 1-day aheadforecasting dropped dramatically however improvement of5-day ahead forecasting with EMD(-1)-MLP models islimited EMD(-2)-MLP models which deduct the twohighest frequency IMF series perform better than EMD(-1)-MLP models in the 5-day ahead forecasting experiment Inthe same way the EMD(-3)-MLP models perform betterwhen the forecasting period is longer than 10 days eresults of EMD-MLPlowast models are shown in Panel C ofTable 2 Although the calculation process is more compli-cated the forecasting performance of EMD-MLPlowast is alwaysbetter than MLP or EMD-MLP models according to the

criterion of NMSE In addition the random walk modelswith and without drifts (the random walk model withoutdrifts predicts that all future values will equal the last ob-served value Given a variable Y the k-step-ahead forecastfrom period t of Y is 1113954Yt+k Yt For the random walk modelwith drifts the k-step-ahead forecast from period t of Y is1113954Yt+k Yt + k1113954d where 1113954d is estimated by the average changeof Yt in the past 60 days) are used to examine the same datae related results in Panel D of Table 2 indicate that for theMLP-EMD and MLP-EMDlowast models their performance isobviously better than the random walk models in mostsituations

Table 3 is based on the forecasting performance of theabove models with Dstat which shows similar experimentalresults to the NMSE criterione table shows that if EMD(-2)-MLP(53)lowast is applied to forecasting the direction of theCNY series 30 days later the hitting rate can be as high as8639 In general although the calculation of EMD-MLPlowast

minus002500000025

c1

minus006minus003

000003006

c2

minus004

000

004

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minus003000003006

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minus004000004008

c5

minus005

000

005

c6

65707580

Resid

ual

0 1000 2000Time

6065707580

Raw

dat

a

Empirical mode decomposition

Figure 4 EMD decomposition of CNY from 2006 to 2015 is shown in this figure including the raw data series 6 IMFs and one residual

Complexity 7

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

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minus002000002

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minus0050minus0025

000000250050

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000003006

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minus010minus005

000005010

c762636465

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ual

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60

62

64

66

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dat

a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 2: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

same price level Craig et al [5] and Funke et al [6] studyCNY-CNH pricing differentials in detail

It is well documented that the exchange rate series isconsidered as nonlinear and nonstationary time series andinteractively influenced by many factors which makes theaccurate forecasting of exchange rate rather challengingDuring past decades traditional econometric and statisticaltechniques including autoregressive integrated movingaverage (ARIMA) cointegration analysis vector autore-gression (VAR) and error correction (ECM) models havebeen widely used in foreign exchange rates forecastingHowever in the real-world financial markets exchange rateseries are nonlinear and rarely form purely linear combi-nations [7ndash10] us the above traditional models alwaysprovide unreliable forecasting if one continue applying thesetraditional econometric and statistical models e mainreason of this deficiency is that traditional econometric andstatistical models are constructed based on linear assump-tions which will be unable to capture the nonlinear featureshidden in the exchange rate series

Considering the limitation of traditional econometricand statistical models many nonlinear artificial intelligencemodels (AI) such as artificial neural networks (ANN)[11 12] feedforward neural networks (FNN) [13 14]support vector regression (SVR) [15ndash17] and genetic pro-gramming (GP) [18 19] have been applied to investigate theforecasting ability of financial time series Yu et al [20]provide a complete review of foreign exchange rate fore-casting with ANN and also introduce SVR and GP How-ever many AI-based models also have their ownshortcomings For instances ANN usually suffers fromoverfitting and local minima while other models includingGP and SVR are sensitive to parameter estimation Recentlydue to the complex characteristics of exchange rate seriesseveral studies show that a single model is unable to captureall the features and make accurate forecasts [21]

To overcome above shortcomings many researchersstart to rely on the hybrid model to forecast exchange rateseries accurately e composite forecasting method allowsus to obtain an approach to the dynamics underlying thedata by combining the predictions obtained from differentindividual techniques Alvarez-Dıaz and Alvarez [22] at-tempt to exploit the nonlinear structure by constructing thegenetic programming and neural networks compositemethod and apply this composite method to forecast YenUS$ and Pound SterlingUS$ exchange rates Other scholarsalso try to improve the forecasting accuracy of exchange rateseries by applying hybrid forecasting models For exampleZhao and Yang [23] andWong et al [24] use fuzzy clusteringand ANN to forecast financial time series Yu et al [25]propose an online big data-driven oil consumption fore-casting model based on Google trend by combining therelationship investigation and prediction improvement Yuet al [14] design a novel ensemble forecasting approach forcomplex time series by coupling sparse representation (SR)and feedforward neural network (FNN) ie the SR-basedFNN approach

e empirical mode decomposition (EMD) technique isfirst proposed by Huang et al [26] From the theoretical

views EMD is suitable for time series data in terms ofdecomposing the original data into components whichcould break the forecasting task down into simpler fore-casting subtasks ese decompositions consist of a finiteand often small number of intrinsic mode functions (IMFs)and one residual From the perspective of financial practicevarious economic activities may cause a different impactperiodicity on the exchange rate for example the companyrsquosfinancial report is released quarterly but government eco-nomic indicators are usually published once a year EMD ispotentially helpful in decomposing these effects and leads toimprove forecasting works ere are several studiesemploying the EMD technique in hybrid models For in-stance Yu et al [27] forecast crude oil prices with an EMD-based neural network model Chen et al [28] also combineEMD and the ANN approach to forecast tourism demandand Lin et al [29] propose a hybrid model using EMD andSVR for foreign exchange rate forecasting In this empiricalexperiment the original CNY or CNH price series withcharacteristics of nonlinearity and nonstationarity are di-vided into several independent subseries by the EMDtechnique and then partial or all IMFs and one residual areused to forecast Tang et al [30] combine the ensembleempirical mode decomposition (EEMD) with randomvector functional link (RVFL) network and find the pro-posed EEMD-based RVFL network performs significantlybetter in terms of prediction accuracy than not only singlealgorithms such as RVFL network extreme learning ma-chine (ELM) kernel ridge regression random forestbackpropagation neural network least square support vectorregression and autoregressive integrated moving averagebut also their respective EEMD-based ensemble variantsWesummarize in Table 1 the main characteristics of thesestudies on individual and hybrid forecasting methods in therecent literature

is study will focus on using ANN to forecast the RMBwith different forecasting horizons of 1 5 10 20 and 30days Nevertheless Huang et al [32] show that ANN per-forms better than the random walk while the forecastinghorizon is less than five days but for longer horizons such as10 and 30 days the general performance of ANN is worsethan the random walk model In this study a type offeedforward artificial neural network model called multi-layer perceptron (MLP) is adopted Empirical studies consistnot only of the pure MLP model but also a hybrid modelwith EMD to improve forecasting performance

In this study the hybrid forecasting model combiningMLP and EMD is similar to the work of Yu et al [27]However this study further considers the influence of IMFsthat have different levels of frequency In concrete termshigher frequency IMFs could be regarded as noise com-ponents when our forecasting horizon is longer Based onthis concept two hybrid models are proposed and namedEMD-MLP and EMD-MLPlowast Comparing these to pureMLP the former adjusts the original time series data bysubtracting higher frequency IMFs and then uses MLP tocompute the one-day ahead predictions e EMD-MLPlowastmodel applies the ldquodivide-and-conquerrdquo principle to con-struct a novel forecasting methodology in which partial or

2 Complexity

all IMFs and one residual are used According to the em-pirical evidence in this study both types of hybrid modelsare superior to the pureMLPmodel whether with 1- 5- 10-20- or 30-day forecasting horizons Moreover the appli-cation of trading strategies is proposed Although thetransaction costs can make the profits practically disappearor become negative as proved by Alvarez Dıaz [31] thisempirical analysis shows that even considering a 03transaction cost in each trade the trading strategy based onEMD-MLP on average produces an annualized profit ex-ceeding 10

In this paper we will investigate RMB exchange rateforecasting and develop the relevant trading strategies basedon the constructed models e main contributions come

from three aspects First this study focuses on the RMBincluding the onshore RMB exchange rate (CNY) and off-shore RMB exchange rate (CNH) We will use daily data toforecast RMB exchange rates with different horizons basedon three types of models ie MLP EMD-MLP and EMD-MLPlowast Second we will consider not only theMLPmodel butalso the hybrid EMD-MLP and EMD-MLPlowast models toimprove forecasting performance It should be noted thatthe EMD-MLPlowast is different from the methodology proposedby Yu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBFinally we will choose the best forecasting models toconstruct the trading strategies by introducing differentcritical numbers and considering different transaction costs

Table 1 Literature on individual and hybrid forecasting models

Study Type Algorithm Data Timerange Criteria

Aladag et al [11] Individual ANN Exchange rates (TLEUR LEUEUR) 2005ndash2012 RMSE

Alvarez-Diaz andAlvarez [18] Individual GP Exchange rates (various pairs) 1971ndash2000 R-square

Alvarez-Dıaz andAlvarez [22] Individual GP ANN Exchange rates (GBPUSD JPY

USD) 1973ndash2002 NMSE SR

Alvarez Dıaz [31] Individual GP Exchange rates (GBPUSD JPYUSD) 1973ndash2002 U-eil value SR

Huang et al [32] Individual ANN Exchange rates (USDGBP USDJPY) 1997ndash2002 RMSE

Kajitani et al [13] Individual ANN Canadian lynx data 1821ndash1934 RMSENeely et al [19] Individual GP Exchange rates (various pairs) 1974ndash1995 Excess returnNikolsko-Rzhevskyy andProdan [33] Individual Markov switching Exchange rates (various pairs) 1983ndash2008 MSE

Wong et al [24] Individual Novel ANN Simulated time series data ndash MAPE NMSEYu et al [16] Individual Least squares SVM Crude oil 2008ndash2015 MAPE

Yu et al [25] Individual Artificial intelligence Global oil consumption 2004ndash2015 PCC AUC RMSEMAPE

Zhang [10] Individual ANN Simulated time series data mdash MSE MAPE

Zhao and Yang [23] Individual CRPSO-based neuronmodel

Simulated time series dataelectroencephalogram data mdash MSE

Cao [15] Hybrid SVM+SOMSunspot data Santa Fe datasets AC and D and the two building

datasetsmdash NMSE RMSE CV

Chen et al [28] Hybrid EMD+ANN Tourism demand 1971ndash2009 MAPE RMSE MAE

Khashei et al [7] Hybrid ARIMA+ANNs+ fuzzy Exchange rates (USDIran rials)gold price 2005ndash2006 MAE MSE

Lin et al [29] Hybrid EMD+SVM Exchange rates (various pairs) 2005ndash2009 MAPE RMSE MAEDS CP CD

Tang et al [30] Hybrid EEMD+RVFL Crude oil 1986ndash2010 MAPE RMSE DSYu et al [12] Hybrid ANN+WD Patient visits 2010ndash2015 RMSE MAPEYu et al [27] Hybrid EMD+ANN Crude oil 1986ndash2006 NMSE DS

Yu et al [17] Hybrid OPL+ SVMQR Ten publicly available datasets mdash Empirical riskquantile property

Yu et al [14] Hybrid Sparserepresentation +ANN Crude oil 1986ndash2013 RMSE MAPE

Zhang [21] Hybrid ARIMA+ANN Wolfrsquos sunspot data Canadian lynxdata and GBPUSD mdash MSE MAE

ANN artificial neural network SVM support vector machine GP genetic programming CRPSO cooperative random learning particle swarm optimizationRVFL random vector functional link OPL orthogonal pinball loss SVMQR SVM quantile regression WD wavelet decomposition SOM self-organizationfeature map RMSE root mean squared error NMSE normalized mean squared error MAE mean absolute error MAPE mean absolute percentage errorCV coefficient of variation PCC percentage correctly classified accuracy AUC area under the receiver operating curve SR success ratio DS directionalsymmetry CP correct uptrend CD correct downtrend

Complexity 3

e remainder of the paper is organized in the followingmanner Section 2 provides a brief description of ANN andEMD e overall forecasting process and model notationsof three kinds of forecasting models are also included in thispart In Section 3 two currency exchange rates of USD toRMB CNY and CNH are used to test the effectiveness ofthe proposed methodology and the selected models areapplied in trading strategies e conclusions drawn fromthis study are presented in Section 4

2 Methodology

21 Artificial Neural Network (ANN) is study considersMLP based on an error backpropagation algorithm Figure 1shows a simple MLP structure with three input nodes (X1X2 and X3) One hidden layer consists of four hidden nodesand one output node (Y) e nodes are organized in layersand are usually fully connected by weights which indicatethe effects of the corresponding nodes In each node of thehidden and output layers all data are firstly processed by theintegration function (also called the summation function)which combines all incoming signals and secondly pro-cessed by the activation function (also called the transferfunction) which transforms the output of the node Ingeneral the amount of the hidden layer is less than 3 due tothe converging restriction

Particularly the MLPmodel is fitted by the training dataand then the testing data and an out-of-sample dataset areused to verify its forecasting performance rough super-vised learning algorithms the parameters (weights and nodeintercepts) are adjusted iteratively by a process of mini-mizing the forecasting error function Formally an MLPwith an input layer with n nodes one hidden layer consistingof J hidden nodes and an output layer with one output nodecalculates the following function

o(x) f w0 + 1113944

J

j1wj middot f w0j + 1113944

n

i1wijxi

⎛⎝ ⎞⎠⎛⎝ ⎞⎠

f w0 + 1113944

J

j1wj middot f w0j + wT

j x1113872 1113873⎛⎝ ⎞⎠

(1)

where x (x1 xn) is the vector of all input variables w0is the intercept of the output node w0j is the intercept of thejth hidden node wj denotes the weight corresponding to thenode starting at the jth hidden node to the output node andwij denotes the weight corresponding to the node starting atith input node to the jth hidden node erefore all hiddenand output nodes calculate the function f(g(z)) where g(middot)

denotes the integration function which is defined asg(z) w0 + wtz and f(middot) denotes the activation functionwhich is often a bounded nondecreasing nonlinear anddifferentiable function In this study the logistic function(f(u) 1(1 + eminus u)) is used as the activation function

Given inputs x and the current weights which areinitialized with random values from a standard normaldistribution the MLP produces an output o(x) en anerror function is defined is study selects the mean squareerror as follows

E 1N

1113944

N

h1oh(x) minus yh( 1113857

2 (2)

where N is the number of data samples and yh is the ob-served output During the iterative training process theabove steps are repeated to adapt all weights until a pre-specified criterion is fulfilled In order to find a local min-imum of the error function the resilient backpropagationalgorithm modifies the weights in the opposite direction ofpartial derivatives According to Riedmiller and Braun [34]the weights are adjusted by the following rule

w(t+1)k w

tk minus η(t)

k middot signzE(t)

zw(t)k

⎛⎝ ⎞⎠ (3)

where t and k index the iteration steps and the weightsrespectively In order to speed up convergence the learningrate η(t)

k increases if the corresponding partial derivativekeeps the same sign otherwise it will decrease

22 EmpiricalModeDecomposition (EMD) In this study wefurther apply EMD to decompose the time series into severalIMFs and remaining residuesese IMFs usually satisfy twoconditions the first is that the number of extrema and zerocrossings must be equal or different by not more than oneSecond the mean value of the envelopes which include bothlocal maxima and minima must be zero at all points

Given the time series data x(t) t 1 2 T Huanget al [26] propose a sifting process to decompose x(t) efirst step is to identify all local maxima and local minima ofx(t) en the upper and lower envelopes are defined byconnecting all local extrema by a spline line Next for allpoints at the envelope the mean value m1

1(t) from upper andlower envelopes is calculated en it follows computationof the first IMF of x(t)

X1

H11

H12

H13

X3

Y

H14

X2

1 1

Input layer Hidden layer Output layer

w1j

w0j

w0

w2j

w3j

w1

w2

w3

w4

Figure 1 An artificial neural network structure with three inputneurons (X1 X2 and X3) one hidden layer consisting of fourhidden neurons (H11 H12 H13 and H14) and one output neuron(Y)

4 Complexity

h11(t) x(t) minus m

11(t) (4)

If h11(t) does not meet the above two conditions this

study then takes h11(t) as a new data series and repeats

procedure (4) us we calculate

h12(t) h

11(t) minus m

12(t) (5)

In this calculation m12(t) is the mean value of the upper

and lower envelopes of h11(t)

Repeating the same procedure until meeting bothconditions we get the first IMF component of x(t) c1(t)that is

c1(t) h1q(t) (6)

e stopping rule indicates that absolute values of theenvelope meanmust be less than the user-specified tolerancelevel In this study the tolerance level is denoted as thestandard deviation of x(t) times 001 Other interestingstopping rules can be found in the works of Huang et al [26]and Huang and Wu [35]

After extracting the component c1(t) from x(t) wedenote another series r1(t) x(t) minus c1(t) which containsall information except c1(t) Huang et al [36] suggest asifting stop criterion that is rn(t) becomes a monotonicfunction or cannot extract more IMFs Finally the timeseries x(t) can be expressed as

x(t) 1113944n

i1ci(t) + rn(t) (7)

where n is the number of IMFs and rn(t) is the final residuewhich represents the central tendency of the data series x(t)ese IMFs are nearly orthogonal to each other and all havemeans of nearly zero According to the above properties it ispossible to forecast all decompositions and summarize theseestimations to predict x(t)

23 Overall Forecasting Process and Model NotationsConsidering the time series pt t 1 2 T we would liketo predict l-day ahead which is denoted as 1113954pt+l In this studythe input variables (past observations) include ptminus 59 ptminus 19ptminus 9 and ptminus 4 to pt which represent the past price levels of60 days 20 days 10 days and the last 5 days respectivelye output is the l-day ahead prediction Formally it couldbe shown as follows

1113954pt+l φ pt ptminus 4 ptminus 9 ptminus 19 ptminus 59w( 1113857 (8)

where φ(middot) is a function determined by neural networktraining and w is a weight vector of all parameters of MLP

ree kinds of forecasting models are adopted in thisstudy e first is the pure MLP model with one and twohidden layers e second is an EMD-MLP model whichuses EMD to subtract some volatile IMFs from the originaldata series and then uses the new data series to calculate thefinal prediction by MLP technology Figure 2 indicates theprocedure of the EMD(-1)-MLP model which means thefirst IMF component is ignored e third kind of model is

named EMD-MLPlowast which generally consists of the fol-lowing four steps

(1) Decompose the original time series into IMF com-ponents and one residual component via EMD

(2) Determine how many IMF components are usedwhich depends on the length of the forecastingperiod

(3) For each chosen IMF and residual component theMLP model is used as a forecasting tool to modelthese components and to make the correspondingprediction

(4) Add all prediction results to one value which can beseen as the final prediction result for the original timeseries

As an example Figure 3 represents the above procedureof the EMD(-1)-MLPlowast model Time series data aredecomposed via EMD and generates n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) In addition toc1(t) we forecast each decomposition and then sum them asthe prediction results for the original time series

3 Empirical Experiments

31 Data Two kinds of currency exchange rates of USD toRMB are considered in this study If the RMB is tradedonshore (in mainland China) it is referred to as CNY and iftraded offshore (mainly in Hong Kong) it is named CNH

MLP

Prediction

hellip

Time series data

EMD

New series data

c1(t) c2(t) cn(t) rn(t)

sum

Figure 2 An example of the EMD(-1)-MLPmodelWe decomposea time series data by the EMD and generate n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) We sum all de-compositions except c1(t) to produce a new time series data enthe MLP is applied to compute the prediction

Complexity 5

Both time series data are downloaded from Bloomberg ForCNY daily data from January 2 2006 to December 21 2015with a total of 2584 observations are examined in this studySince the CNH officially commenced on July 19 2010 itssample period is from January 3 2011 to December 21 2015with a total of 1304 observations For training the neuralnetwork models two-thirds of the observations are ran-domly assigned to the training dataset and the remainder isused as the testing dataset In addition it should be notedthat the time series in price levels is used in the followinganalysis rather than in return levels

According to descriptions shown in Section 32 theEMD technique is used to decompose both CNY and CNHprice series into several independent IMFs and one residualcomponent e decomposed results of CNY and CNH arerepresented in Figures 4 and 5 Comparing these two figuresthe original data series and decompositions seem dissimilarwhich is due to the different lengths of the sample periods Infact their IMFs have some similar characteristics Firstfocusing on the sample period 2011ndash2015 their residualcomponents have the same trend Starting at about 65 theydrop slightly to 62 and then rise slightly to 65 Second theswing period of high-frequency IMFs is shorter and also themean of absolute values of high-frequency IMFs is smallerwhen compared with low frequency For example in theseries of CNY the absolute values of c1 c3 and c5 are000298 000596 and 002002 respectively In our estima-tion model it is not necessary to include all the high-fre-quency IMFs as considering high-frequency IMFs may

reduce the forecasting accuracy when the forecasting periodis long erefore in the model EMD-MLP the high-fre-quency IMF is removed to get the denoised time series Inthe model EMD-MLPlowast not only are all the decompositionschosen to forecast the exchange rate but consideration isalso given to using part of the decompositions to conductforecasting discarding the high-frequency IMF series

32 Experimental Results Two main criteria are consideredin this empirical experiment the normalized mean squarederror (NMSE) and the directional statistic (Dstat) to eval-uate the levels of prediction and directional forecastingrespectively Typically following [37] the NMSE is definedby

NMSE 1σ2Ψ

1Nt

1113944sisinΨ

1113954ps+l minus ps+l( 11138572 (9)

where Ψ refers to the test dataset containing Nt observa-tions 1113954ps+l is the l-day ahead prediction ps+l is the actualvalue and σ2Ψ is the variance of ps+l Clearly the NMSE isone of the most important criteria for measuring the validityof the forecasting model but from a business perspectiveimproving the accuracy of directional predictions cansupport decision-making so as to generate greater profitsFurthermore the Diebold-Mariano (DM) test [38] isadopted to investigate whether adding EMD could improvethe forecasting performance of the MLP model Specificallythe null hypothesis is that the EMD-MLP (or EMD-MLPlowast)model has a lower forecast accuracy than the correspondingMLP model For example in the case of the EMD(-1)-MLP(53) the corresponding model infers the MLP(53)model

Besides the NMSE evaluation the directional statistic(Dstat) is applied to measure the ability to predict movementdirection [27 39] which can be expressed as

Dstat 1

Nt

1113944sisinΨ

as times 100 (10)

where as 1 if (1113954ps+l minus ps)(ps+l minus ps)ge 0 and as 0 other-wise Pesaran and Timmermann [40] provide the directionalaccuracy (DAC) test to examine predictive performance Inthis case the DAC test is used to determine whether Dstat issignificantly larger than 05 We have also adopted the excessprofitability test proposed by Anatolyev and Gerko [41] inevery related empirical study Since both tests produce thesame outcome we only report the results of DAC tests in thefollowing empirical studies

Table 2 compares the forecasting performance in termsof the NMSE for the MLP EMD-MLP and EMD-MLPlowastmodels e NMSE is reported as the percentage for l-dayahead predictions where l 1 5 10 20 and 30 For eachprediction period the minimumNMSE is designated in boldfont Panel A of Table 2 displays the experimental results ofthe MLP models It is clear that with the increase inforecasting period the NMSE becomes larger suggestingreduced forecasting accuracy for a longer forecasting periodAlso the more complex MLPmodels with two hidden layers

MLP

Prediction

MLP MLPhellip

Time series data

EMD

c1(t) c2(t)

c2(t)

cn(t)

cn(t)

sum

rn(t)

rn(t)ˆ ˆ ˆ

Figure 3 An example of the EMD(-1)-MLPlowast model We de-compose a time series data by the EMD and generate n IMFcomponents c1(t) c2(t) cn(t) and one residue rn(t) Besidesc1(t) we forecast each decomposition and them sum them as theprediction

6 Complexity

do not offer better forecasting accuracy and are even worsefor 1-day ahead prediction

e empirical results of EMD-MLP are discussed inPanel B of Table 2 EMD(-1)-MLP treats the highest fre-quency IMF c1 as noise and applies the MLP model aftersubtracting the c1 series from the original time seriesEmpirical results show that the NMSE of 1-day aheadforecasting dropped dramatically however improvement of5-day ahead forecasting with EMD(-1)-MLP models islimited EMD(-2)-MLP models which deduct the twohighest frequency IMF series perform better than EMD(-1)-MLP models in the 5-day ahead forecasting experiment Inthe same way the EMD(-3)-MLP models perform betterwhen the forecasting period is longer than 10 days eresults of EMD-MLPlowast models are shown in Panel C ofTable 2 Although the calculation process is more compli-cated the forecasting performance of EMD-MLPlowast is alwaysbetter than MLP or EMD-MLP models according to the

criterion of NMSE In addition the random walk modelswith and without drifts (the random walk model withoutdrifts predicts that all future values will equal the last ob-served value Given a variable Y the k-step-ahead forecastfrom period t of Y is 1113954Yt+k Yt For the random walk modelwith drifts the k-step-ahead forecast from period t of Y is1113954Yt+k Yt + k1113954d where 1113954d is estimated by the average changeof Yt in the past 60 days) are used to examine the same datae related results in Panel D of Table 2 indicate that for theMLP-EMD and MLP-EMDlowast models their performance isobviously better than the random walk models in mostsituations

Table 3 is based on the forecasting performance of theabove models with Dstat which shows similar experimentalresults to the NMSE criterione table shows that if EMD(-2)-MLP(53)lowast is applied to forecasting the direction of theCNY series 30 days later the hitting rate can be as high as8639 In general although the calculation of EMD-MLPlowast

minus002500000025

c1

minus006minus003

000003006

c2

minus004

000

004

c3

minus003000003006

c4

minus004000004008

c5

minus005

000

005

c6

65707580

Resid

ual

0 1000 2000Time

6065707580

Raw

dat

a

Empirical mode decomposition

Figure 4 EMD decomposition of CNY from 2006 to 2015 is shown in this figure including the raw data series 6 IMFs and one residual

Complexity 7

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

c1

minus002000002

c2

minus0050minus0025

000000250050

c3

minus006minus003

000003006

c4

minus004000004008

c5

minus004000004008

c6

minus010minus005

000005010

c762636465

Resid

ual

0 500 1000Time

60

62

64

66

Raw

dat

a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 3: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

all IMFs and one residual are used According to the em-pirical evidence in this study both types of hybrid modelsare superior to the pureMLPmodel whether with 1- 5- 10-20- or 30-day forecasting horizons Moreover the appli-cation of trading strategies is proposed Although thetransaction costs can make the profits practically disappearor become negative as proved by Alvarez Dıaz [31] thisempirical analysis shows that even considering a 03transaction cost in each trade the trading strategy based onEMD-MLP on average produces an annualized profit ex-ceeding 10

In this paper we will investigate RMB exchange rateforecasting and develop the relevant trading strategies basedon the constructed models e main contributions come

from three aspects First this study focuses on the RMBincluding the onshore RMB exchange rate (CNY) and off-shore RMB exchange rate (CNH) We will use daily data toforecast RMB exchange rates with different horizons basedon three types of models ie MLP EMD-MLP and EMD-MLPlowast Second we will consider not only theMLPmodel butalso the hybrid EMD-MLP and EMD-MLPlowast models toimprove forecasting performance It should be noted thatthe EMD-MLPlowast is different from the methodology proposedby Yu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBFinally we will choose the best forecasting models toconstruct the trading strategies by introducing differentcritical numbers and considering different transaction costs

Table 1 Literature on individual and hybrid forecasting models

Study Type Algorithm Data Timerange Criteria

Aladag et al [11] Individual ANN Exchange rates (TLEUR LEUEUR) 2005ndash2012 RMSE

Alvarez-Diaz andAlvarez [18] Individual GP Exchange rates (various pairs) 1971ndash2000 R-square

Alvarez-Dıaz andAlvarez [22] Individual GP ANN Exchange rates (GBPUSD JPY

USD) 1973ndash2002 NMSE SR

Alvarez Dıaz [31] Individual GP Exchange rates (GBPUSD JPYUSD) 1973ndash2002 U-eil value SR

Huang et al [32] Individual ANN Exchange rates (USDGBP USDJPY) 1997ndash2002 RMSE

Kajitani et al [13] Individual ANN Canadian lynx data 1821ndash1934 RMSENeely et al [19] Individual GP Exchange rates (various pairs) 1974ndash1995 Excess returnNikolsko-Rzhevskyy andProdan [33] Individual Markov switching Exchange rates (various pairs) 1983ndash2008 MSE

Wong et al [24] Individual Novel ANN Simulated time series data ndash MAPE NMSEYu et al [16] Individual Least squares SVM Crude oil 2008ndash2015 MAPE

Yu et al [25] Individual Artificial intelligence Global oil consumption 2004ndash2015 PCC AUC RMSEMAPE

Zhang [10] Individual ANN Simulated time series data mdash MSE MAPE

Zhao and Yang [23] Individual CRPSO-based neuronmodel

Simulated time series dataelectroencephalogram data mdash MSE

Cao [15] Hybrid SVM+SOMSunspot data Santa Fe datasets AC and D and the two building

datasetsmdash NMSE RMSE CV

Chen et al [28] Hybrid EMD+ANN Tourism demand 1971ndash2009 MAPE RMSE MAE

Khashei et al [7] Hybrid ARIMA+ANNs+ fuzzy Exchange rates (USDIran rials)gold price 2005ndash2006 MAE MSE

Lin et al [29] Hybrid EMD+SVM Exchange rates (various pairs) 2005ndash2009 MAPE RMSE MAEDS CP CD

Tang et al [30] Hybrid EEMD+RVFL Crude oil 1986ndash2010 MAPE RMSE DSYu et al [12] Hybrid ANN+WD Patient visits 2010ndash2015 RMSE MAPEYu et al [27] Hybrid EMD+ANN Crude oil 1986ndash2006 NMSE DS

Yu et al [17] Hybrid OPL+ SVMQR Ten publicly available datasets mdash Empirical riskquantile property

Yu et al [14] Hybrid Sparserepresentation +ANN Crude oil 1986ndash2013 RMSE MAPE

Zhang [21] Hybrid ARIMA+ANN Wolfrsquos sunspot data Canadian lynxdata and GBPUSD mdash MSE MAE

ANN artificial neural network SVM support vector machine GP genetic programming CRPSO cooperative random learning particle swarm optimizationRVFL random vector functional link OPL orthogonal pinball loss SVMQR SVM quantile regression WD wavelet decomposition SOM self-organizationfeature map RMSE root mean squared error NMSE normalized mean squared error MAE mean absolute error MAPE mean absolute percentage errorCV coefficient of variation PCC percentage correctly classified accuracy AUC area under the receiver operating curve SR success ratio DS directionalsymmetry CP correct uptrend CD correct downtrend

Complexity 3

e remainder of the paper is organized in the followingmanner Section 2 provides a brief description of ANN andEMD e overall forecasting process and model notationsof three kinds of forecasting models are also included in thispart In Section 3 two currency exchange rates of USD toRMB CNY and CNH are used to test the effectiveness ofthe proposed methodology and the selected models areapplied in trading strategies e conclusions drawn fromthis study are presented in Section 4

2 Methodology

21 Artificial Neural Network (ANN) is study considersMLP based on an error backpropagation algorithm Figure 1shows a simple MLP structure with three input nodes (X1X2 and X3) One hidden layer consists of four hidden nodesand one output node (Y) e nodes are organized in layersand are usually fully connected by weights which indicatethe effects of the corresponding nodes In each node of thehidden and output layers all data are firstly processed by theintegration function (also called the summation function)which combines all incoming signals and secondly pro-cessed by the activation function (also called the transferfunction) which transforms the output of the node Ingeneral the amount of the hidden layer is less than 3 due tothe converging restriction

Particularly the MLPmodel is fitted by the training dataand then the testing data and an out-of-sample dataset areused to verify its forecasting performance rough super-vised learning algorithms the parameters (weights and nodeintercepts) are adjusted iteratively by a process of mini-mizing the forecasting error function Formally an MLPwith an input layer with n nodes one hidden layer consistingof J hidden nodes and an output layer with one output nodecalculates the following function

o(x) f w0 + 1113944

J

j1wj middot f w0j + 1113944

n

i1wijxi

⎛⎝ ⎞⎠⎛⎝ ⎞⎠

f w0 + 1113944

J

j1wj middot f w0j + wT

j x1113872 1113873⎛⎝ ⎞⎠

(1)

where x (x1 xn) is the vector of all input variables w0is the intercept of the output node w0j is the intercept of thejth hidden node wj denotes the weight corresponding to thenode starting at the jth hidden node to the output node andwij denotes the weight corresponding to the node starting atith input node to the jth hidden node erefore all hiddenand output nodes calculate the function f(g(z)) where g(middot)

denotes the integration function which is defined asg(z) w0 + wtz and f(middot) denotes the activation functionwhich is often a bounded nondecreasing nonlinear anddifferentiable function In this study the logistic function(f(u) 1(1 + eminus u)) is used as the activation function

Given inputs x and the current weights which areinitialized with random values from a standard normaldistribution the MLP produces an output o(x) en anerror function is defined is study selects the mean squareerror as follows

E 1N

1113944

N

h1oh(x) minus yh( 1113857

2 (2)

where N is the number of data samples and yh is the ob-served output During the iterative training process theabove steps are repeated to adapt all weights until a pre-specified criterion is fulfilled In order to find a local min-imum of the error function the resilient backpropagationalgorithm modifies the weights in the opposite direction ofpartial derivatives According to Riedmiller and Braun [34]the weights are adjusted by the following rule

w(t+1)k w

tk minus η(t)

k middot signzE(t)

zw(t)k

⎛⎝ ⎞⎠ (3)

where t and k index the iteration steps and the weightsrespectively In order to speed up convergence the learningrate η(t)

k increases if the corresponding partial derivativekeeps the same sign otherwise it will decrease

22 EmpiricalModeDecomposition (EMD) In this study wefurther apply EMD to decompose the time series into severalIMFs and remaining residuesese IMFs usually satisfy twoconditions the first is that the number of extrema and zerocrossings must be equal or different by not more than oneSecond the mean value of the envelopes which include bothlocal maxima and minima must be zero at all points

Given the time series data x(t) t 1 2 T Huanget al [26] propose a sifting process to decompose x(t) efirst step is to identify all local maxima and local minima ofx(t) en the upper and lower envelopes are defined byconnecting all local extrema by a spline line Next for allpoints at the envelope the mean value m1

1(t) from upper andlower envelopes is calculated en it follows computationof the first IMF of x(t)

X1

H11

H12

H13

X3

Y

H14

X2

1 1

Input layer Hidden layer Output layer

w1j

w0j

w0

w2j

w3j

w1

w2

w3

w4

Figure 1 An artificial neural network structure with three inputneurons (X1 X2 and X3) one hidden layer consisting of fourhidden neurons (H11 H12 H13 and H14) and one output neuron(Y)

4 Complexity

h11(t) x(t) minus m

11(t) (4)

If h11(t) does not meet the above two conditions this

study then takes h11(t) as a new data series and repeats

procedure (4) us we calculate

h12(t) h

11(t) minus m

12(t) (5)

In this calculation m12(t) is the mean value of the upper

and lower envelopes of h11(t)

Repeating the same procedure until meeting bothconditions we get the first IMF component of x(t) c1(t)that is

c1(t) h1q(t) (6)

e stopping rule indicates that absolute values of theenvelope meanmust be less than the user-specified tolerancelevel In this study the tolerance level is denoted as thestandard deviation of x(t) times 001 Other interestingstopping rules can be found in the works of Huang et al [26]and Huang and Wu [35]

After extracting the component c1(t) from x(t) wedenote another series r1(t) x(t) minus c1(t) which containsall information except c1(t) Huang et al [36] suggest asifting stop criterion that is rn(t) becomes a monotonicfunction or cannot extract more IMFs Finally the timeseries x(t) can be expressed as

x(t) 1113944n

i1ci(t) + rn(t) (7)

where n is the number of IMFs and rn(t) is the final residuewhich represents the central tendency of the data series x(t)ese IMFs are nearly orthogonal to each other and all havemeans of nearly zero According to the above properties it ispossible to forecast all decompositions and summarize theseestimations to predict x(t)

23 Overall Forecasting Process and Model NotationsConsidering the time series pt t 1 2 T we would liketo predict l-day ahead which is denoted as 1113954pt+l In this studythe input variables (past observations) include ptminus 59 ptminus 19ptminus 9 and ptminus 4 to pt which represent the past price levels of60 days 20 days 10 days and the last 5 days respectivelye output is the l-day ahead prediction Formally it couldbe shown as follows

1113954pt+l φ pt ptminus 4 ptminus 9 ptminus 19 ptminus 59w( 1113857 (8)

where φ(middot) is a function determined by neural networktraining and w is a weight vector of all parameters of MLP

ree kinds of forecasting models are adopted in thisstudy e first is the pure MLP model with one and twohidden layers e second is an EMD-MLP model whichuses EMD to subtract some volatile IMFs from the originaldata series and then uses the new data series to calculate thefinal prediction by MLP technology Figure 2 indicates theprocedure of the EMD(-1)-MLP model which means thefirst IMF component is ignored e third kind of model is

named EMD-MLPlowast which generally consists of the fol-lowing four steps

(1) Decompose the original time series into IMF com-ponents and one residual component via EMD

(2) Determine how many IMF components are usedwhich depends on the length of the forecastingperiod

(3) For each chosen IMF and residual component theMLP model is used as a forecasting tool to modelthese components and to make the correspondingprediction

(4) Add all prediction results to one value which can beseen as the final prediction result for the original timeseries

As an example Figure 3 represents the above procedureof the EMD(-1)-MLPlowast model Time series data aredecomposed via EMD and generates n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) In addition toc1(t) we forecast each decomposition and then sum them asthe prediction results for the original time series

3 Empirical Experiments

31 Data Two kinds of currency exchange rates of USD toRMB are considered in this study If the RMB is tradedonshore (in mainland China) it is referred to as CNY and iftraded offshore (mainly in Hong Kong) it is named CNH

MLP

Prediction

hellip

Time series data

EMD

New series data

c1(t) c2(t) cn(t) rn(t)

sum

Figure 2 An example of the EMD(-1)-MLPmodelWe decomposea time series data by the EMD and generate n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) We sum all de-compositions except c1(t) to produce a new time series data enthe MLP is applied to compute the prediction

Complexity 5

Both time series data are downloaded from Bloomberg ForCNY daily data from January 2 2006 to December 21 2015with a total of 2584 observations are examined in this studySince the CNH officially commenced on July 19 2010 itssample period is from January 3 2011 to December 21 2015with a total of 1304 observations For training the neuralnetwork models two-thirds of the observations are ran-domly assigned to the training dataset and the remainder isused as the testing dataset In addition it should be notedthat the time series in price levels is used in the followinganalysis rather than in return levels

According to descriptions shown in Section 32 theEMD technique is used to decompose both CNY and CNHprice series into several independent IMFs and one residualcomponent e decomposed results of CNY and CNH arerepresented in Figures 4 and 5 Comparing these two figuresthe original data series and decompositions seem dissimilarwhich is due to the different lengths of the sample periods Infact their IMFs have some similar characteristics Firstfocusing on the sample period 2011ndash2015 their residualcomponents have the same trend Starting at about 65 theydrop slightly to 62 and then rise slightly to 65 Second theswing period of high-frequency IMFs is shorter and also themean of absolute values of high-frequency IMFs is smallerwhen compared with low frequency For example in theseries of CNY the absolute values of c1 c3 and c5 are000298 000596 and 002002 respectively In our estima-tion model it is not necessary to include all the high-fre-quency IMFs as considering high-frequency IMFs may

reduce the forecasting accuracy when the forecasting periodis long erefore in the model EMD-MLP the high-fre-quency IMF is removed to get the denoised time series Inthe model EMD-MLPlowast not only are all the decompositionschosen to forecast the exchange rate but consideration isalso given to using part of the decompositions to conductforecasting discarding the high-frequency IMF series

32 Experimental Results Two main criteria are consideredin this empirical experiment the normalized mean squarederror (NMSE) and the directional statistic (Dstat) to eval-uate the levels of prediction and directional forecastingrespectively Typically following [37] the NMSE is definedby

NMSE 1σ2Ψ

1Nt

1113944sisinΨ

1113954ps+l minus ps+l( 11138572 (9)

where Ψ refers to the test dataset containing Nt observa-tions 1113954ps+l is the l-day ahead prediction ps+l is the actualvalue and σ2Ψ is the variance of ps+l Clearly the NMSE isone of the most important criteria for measuring the validityof the forecasting model but from a business perspectiveimproving the accuracy of directional predictions cansupport decision-making so as to generate greater profitsFurthermore the Diebold-Mariano (DM) test [38] isadopted to investigate whether adding EMD could improvethe forecasting performance of the MLP model Specificallythe null hypothesis is that the EMD-MLP (or EMD-MLPlowast)model has a lower forecast accuracy than the correspondingMLP model For example in the case of the EMD(-1)-MLP(53) the corresponding model infers the MLP(53)model

Besides the NMSE evaluation the directional statistic(Dstat) is applied to measure the ability to predict movementdirection [27 39] which can be expressed as

Dstat 1

Nt

1113944sisinΨ

as times 100 (10)

where as 1 if (1113954ps+l minus ps)(ps+l minus ps)ge 0 and as 0 other-wise Pesaran and Timmermann [40] provide the directionalaccuracy (DAC) test to examine predictive performance Inthis case the DAC test is used to determine whether Dstat issignificantly larger than 05 We have also adopted the excessprofitability test proposed by Anatolyev and Gerko [41] inevery related empirical study Since both tests produce thesame outcome we only report the results of DAC tests in thefollowing empirical studies

Table 2 compares the forecasting performance in termsof the NMSE for the MLP EMD-MLP and EMD-MLPlowastmodels e NMSE is reported as the percentage for l-dayahead predictions where l 1 5 10 20 and 30 For eachprediction period the minimumNMSE is designated in boldfont Panel A of Table 2 displays the experimental results ofthe MLP models It is clear that with the increase inforecasting period the NMSE becomes larger suggestingreduced forecasting accuracy for a longer forecasting periodAlso the more complex MLPmodels with two hidden layers

MLP

Prediction

MLP MLPhellip

Time series data

EMD

c1(t) c2(t)

c2(t)

cn(t)

cn(t)

sum

rn(t)

rn(t)ˆ ˆ ˆ

Figure 3 An example of the EMD(-1)-MLPlowast model We de-compose a time series data by the EMD and generate n IMFcomponents c1(t) c2(t) cn(t) and one residue rn(t) Besidesc1(t) we forecast each decomposition and them sum them as theprediction

6 Complexity

do not offer better forecasting accuracy and are even worsefor 1-day ahead prediction

e empirical results of EMD-MLP are discussed inPanel B of Table 2 EMD(-1)-MLP treats the highest fre-quency IMF c1 as noise and applies the MLP model aftersubtracting the c1 series from the original time seriesEmpirical results show that the NMSE of 1-day aheadforecasting dropped dramatically however improvement of5-day ahead forecasting with EMD(-1)-MLP models islimited EMD(-2)-MLP models which deduct the twohighest frequency IMF series perform better than EMD(-1)-MLP models in the 5-day ahead forecasting experiment Inthe same way the EMD(-3)-MLP models perform betterwhen the forecasting period is longer than 10 days eresults of EMD-MLPlowast models are shown in Panel C ofTable 2 Although the calculation process is more compli-cated the forecasting performance of EMD-MLPlowast is alwaysbetter than MLP or EMD-MLP models according to the

criterion of NMSE In addition the random walk modelswith and without drifts (the random walk model withoutdrifts predicts that all future values will equal the last ob-served value Given a variable Y the k-step-ahead forecastfrom period t of Y is 1113954Yt+k Yt For the random walk modelwith drifts the k-step-ahead forecast from period t of Y is1113954Yt+k Yt + k1113954d where 1113954d is estimated by the average changeof Yt in the past 60 days) are used to examine the same datae related results in Panel D of Table 2 indicate that for theMLP-EMD and MLP-EMDlowast models their performance isobviously better than the random walk models in mostsituations

Table 3 is based on the forecasting performance of theabove models with Dstat which shows similar experimentalresults to the NMSE criterione table shows that if EMD(-2)-MLP(53)lowast is applied to forecasting the direction of theCNY series 30 days later the hitting rate can be as high as8639 In general although the calculation of EMD-MLPlowast

minus002500000025

c1

minus006minus003

000003006

c2

minus004

000

004

c3

minus003000003006

c4

minus004000004008

c5

minus005

000

005

c6

65707580

Resid

ual

0 1000 2000Time

6065707580

Raw

dat

a

Empirical mode decomposition

Figure 4 EMD decomposition of CNY from 2006 to 2015 is shown in this figure including the raw data series 6 IMFs and one residual

Complexity 7

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

c1

minus002000002

c2

minus0050minus0025

000000250050

c3

minus006minus003

000003006

c4

minus004000004008

c5

minus004000004008

c6

minus010minus005

000005010

c762636465

Resid

ual

0 500 1000Time

60

62

64

66

Raw

dat

a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 4: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

e remainder of the paper is organized in the followingmanner Section 2 provides a brief description of ANN andEMD e overall forecasting process and model notationsof three kinds of forecasting models are also included in thispart In Section 3 two currency exchange rates of USD toRMB CNY and CNH are used to test the effectiveness ofthe proposed methodology and the selected models areapplied in trading strategies e conclusions drawn fromthis study are presented in Section 4

2 Methodology

21 Artificial Neural Network (ANN) is study considersMLP based on an error backpropagation algorithm Figure 1shows a simple MLP structure with three input nodes (X1X2 and X3) One hidden layer consists of four hidden nodesand one output node (Y) e nodes are organized in layersand are usually fully connected by weights which indicatethe effects of the corresponding nodes In each node of thehidden and output layers all data are firstly processed by theintegration function (also called the summation function)which combines all incoming signals and secondly pro-cessed by the activation function (also called the transferfunction) which transforms the output of the node Ingeneral the amount of the hidden layer is less than 3 due tothe converging restriction

Particularly the MLPmodel is fitted by the training dataand then the testing data and an out-of-sample dataset areused to verify its forecasting performance rough super-vised learning algorithms the parameters (weights and nodeintercepts) are adjusted iteratively by a process of mini-mizing the forecasting error function Formally an MLPwith an input layer with n nodes one hidden layer consistingof J hidden nodes and an output layer with one output nodecalculates the following function

o(x) f w0 + 1113944

J

j1wj middot f w0j + 1113944

n

i1wijxi

⎛⎝ ⎞⎠⎛⎝ ⎞⎠

f w0 + 1113944

J

j1wj middot f w0j + wT

j x1113872 1113873⎛⎝ ⎞⎠

(1)

where x (x1 xn) is the vector of all input variables w0is the intercept of the output node w0j is the intercept of thejth hidden node wj denotes the weight corresponding to thenode starting at the jth hidden node to the output node andwij denotes the weight corresponding to the node starting atith input node to the jth hidden node erefore all hiddenand output nodes calculate the function f(g(z)) where g(middot)

denotes the integration function which is defined asg(z) w0 + wtz and f(middot) denotes the activation functionwhich is often a bounded nondecreasing nonlinear anddifferentiable function In this study the logistic function(f(u) 1(1 + eminus u)) is used as the activation function

Given inputs x and the current weights which areinitialized with random values from a standard normaldistribution the MLP produces an output o(x) en anerror function is defined is study selects the mean squareerror as follows

E 1N

1113944

N

h1oh(x) minus yh( 1113857

2 (2)

where N is the number of data samples and yh is the ob-served output During the iterative training process theabove steps are repeated to adapt all weights until a pre-specified criterion is fulfilled In order to find a local min-imum of the error function the resilient backpropagationalgorithm modifies the weights in the opposite direction ofpartial derivatives According to Riedmiller and Braun [34]the weights are adjusted by the following rule

w(t+1)k w

tk minus η(t)

k middot signzE(t)

zw(t)k

⎛⎝ ⎞⎠ (3)

where t and k index the iteration steps and the weightsrespectively In order to speed up convergence the learningrate η(t)

k increases if the corresponding partial derivativekeeps the same sign otherwise it will decrease

22 EmpiricalModeDecomposition (EMD) In this study wefurther apply EMD to decompose the time series into severalIMFs and remaining residuesese IMFs usually satisfy twoconditions the first is that the number of extrema and zerocrossings must be equal or different by not more than oneSecond the mean value of the envelopes which include bothlocal maxima and minima must be zero at all points

Given the time series data x(t) t 1 2 T Huanget al [26] propose a sifting process to decompose x(t) efirst step is to identify all local maxima and local minima ofx(t) en the upper and lower envelopes are defined byconnecting all local extrema by a spline line Next for allpoints at the envelope the mean value m1

1(t) from upper andlower envelopes is calculated en it follows computationof the first IMF of x(t)

X1

H11

H12

H13

X3

Y

H14

X2

1 1

Input layer Hidden layer Output layer

w1j

w0j

w0

w2j

w3j

w1

w2

w3

w4

Figure 1 An artificial neural network structure with three inputneurons (X1 X2 and X3) one hidden layer consisting of fourhidden neurons (H11 H12 H13 and H14) and one output neuron(Y)

4 Complexity

h11(t) x(t) minus m

11(t) (4)

If h11(t) does not meet the above two conditions this

study then takes h11(t) as a new data series and repeats

procedure (4) us we calculate

h12(t) h

11(t) minus m

12(t) (5)

In this calculation m12(t) is the mean value of the upper

and lower envelopes of h11(t)

Repeating the same procedure until meeting bothconditions we get the first IMF component of x(t) c1(t)that is

c1(t) h1q(t) (6)

e stopping rule indicates that absolute values of theenvelope meanmust be less than the user-specified tolerancelevel In this study the tolerance level is denoted as thestandard deviation of x(t) times 001 Other interestingstopping rules can be found in the works of Huang et al [26]and Huang and Wu [35]

After extracting the component c1(t) from x(t) wedenote another series r1(t) x(t) minus c1(t) which containsall information except c1(t) Huang et al [36] suggest asifting stop criterion that is rn(t) becomes a monotonicfunction or cannot extract more IMFs Finally the timeseries x(t) can be expressed as

x(t) 1113944n

i1ci(t) + rn(t) (7)

where n is the number of IMFs and rn(t) is the final residuewhich represents the central tendency of the data series x(t)ese IMFs are nearly orthogonal to each other and all havemeans of nearly zero According to the above properties it ispossible to forecast all decompositions and summarize theseestimations to predict x(t)

23 Overall Forecasting Process and Model NotationsConsidering the time series pt t 1 2 T we would liketo predict l-day ahead which is denoted as 1113954pt+l In this studythe input variables (past observations) include ptminus 59 ptminus 19ptminus 9 and ptminus 4 to pt which represent the past price levels of60 days 20 days 10 days and the last 5 days respectivelye output is the l-day ahead prediction Formally it couldbe shown as follows

1113954pt+l φ pt ptminus 4 ptminus 9 ptminus 19 ptminus 59w( 1113857 (8)

where φ(middot) is a function determined by neural networktraining and w is a weight vector of all parameters of MLP

ree kinds of forecasting models are adopted in thisstudy e first is the pure MLP model with one and twohidden layers e second is an EMD-MLP model whichuses EMD to subtract some volatile IMFs from the originaldata series and then uses the new data series to calculate thefinal prediction by MLP technology Figure 2 indicates theprocedure of the EMD(-1)-MLP model which means thefirst IMF component is ignored e third kind of model is

named EMD-MLPlowast which generally consists of the fol-lowing four steps

(1) Decompose the original time series into IMF com-ponents and one residual component via EMD

(2) Determine how many IMF components are usedwhich depends on the length of the forecastingperiod

(3) For each chosen IMF and residual component theMLP model is used as a forecasting tool to modelthese components and to make the correspondingprediction

(4) Add all prediction results to one value which can beseen as the final prediction result for the original timeseries

As an example Figure 3 represents the above procedureof the EMD(-1)-MLPlowast model Time series data aredecomposed via EMD and generates n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) In addition toc1(t) we forecast each decomposition and then sum them asthe prediction results for the original time series

3 Empirical Experiments

31 Data Two kinds of currency exchange rates of USD toRMB are considered in this study If the RMB is tradedonshore (in mainland China) it is referred to as CNY and iftraded offshore (mainly in Hong Kong) it is named CNH

MLP

Prediction

hellip

Time series data

EMD

New series data

c1(t) c2(t) cn(t) rn(t)

sum

Figure 2 An example of the EMD(-1)-MLPmodelWe decomposea time series data by the EMD and generate n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) We sum all de-compositions except c1(t) to produce a new time series data enthe MLP is applied to compute the prediction

Complexity 5

Both time series data are downloaded from Bloomberg ForCNY daily data from January 2 2006 to December 21 2015with a total of 2584 observations are examined in this studySince the CNH officially commenced on July 19 2010 itssample period is from January 3 2011 to December 21 2015with a total of 1304 observations For training the neuralnetwork models two-thirds of the observations are ran-domly assigned to the training dataset and the remainder isused as the testing dataset In addition it should be notedthat the time series in price levels is used in the followinganalysis rather than in return levels

According to descriptions shown in Section 32 theEMD technique is used to decompose both CNY and CNHprice series into several independent IMFs and one residualcomponent e decomposed results of CNY and CNH arerepresented in Figures 4 and 5 Comparing these two figuresthe original data series and decompositions seem dissimilarwhich is due to the different lengths of the sample periods Infact their IMFs have some similar characteristics Firstfocusing on the sample period 2011ndash2015 their residualcomponents have the same trend Starting at about 65 theydrop slightly to 62 and then rise slightly to 65 Second theswing period of high-frequency IMFs is shorter and also themean of absolute values of high-frequency IMFs is smallerwhen compared with low frequency For example in theseries of CNY the absolute values of c1 c3 and c5 are000298 000596 and 002002 respectively In our estima-tion model it is not necessary to include all the high-fre-quency IMFs as considering high-frequency IMFs may

reduce the forecasting accuracy when the forecasting periodis long erefore in the model EMD-MLP the high-fre-quency IMF is removed to get the denoised time series Inthe model EMD-MLPlowast not only are all the decompositionschosen to forecast the exchange rate but consideration isalso given to using part of the decompositions to conductforecasting discarding the high-frequency IMF series

32 Experimental Results Two main criteria are consideredin this empirical experiment the normalized mean squarederror (NMSE) and the directional statistic (Dstat) to eval-uate the levels of prediction and directional forecastingrespectively Typically following [37] the NMSE is definedby

NMSE 1σ2Ψ

1Nt

1113944sisinΨ

1113954ps+l minus ps+l( 11138572 (9)

where Ψ refers to the test dataset containing Nt observa-tions 1113954ps+l is the l-day ahead prediction ps+l is the actualvalue and σ2Ψ is the variance of ps+l Clearly the NMSE isone of the most important criteria for measuring the validityof the forecasting model but from a business perspectiveimproving the accuracy of directional predictions cansupport decision-making so as to generate greater profitsFurthermore the Diebold-Mariano (DM) test [38] isadopted to investigate whether adding EMD could improvethe forecasting performance of the MLP model Specificallythe null hypothesis is that the EMD-MLP (or EMD-MLPlowast)model has a lower forecast accuracy than the correspondingMLP model For example in the case of the EMD(-1)-MLP(53) the corresponding model infers the MLP(53)model

Besides the NMSE evaluation the directional statistic(Dstat) is applied to measure the ability to predict movementdirection [27 39] which can be expressed as

Dstat 1

Nt

1113944sisinΨ

as times 100 (10)

where as 1 if (1113954ps+l minus ps)(ps+l minus ps)ge 0 and as 0 other-wise Pesaran and Timmermann [40] provide the directionalaccuracy (DAC) test to examine predictive performance Inthis case the DAC test is used to determine whether Dstat issignificantly larger than 05 We have also adopted the excessprofitability test proposed by Anatolyev and Gerko [41] inevery related empirical study Since both tests produce thesame outcome we only report the results of DAC tests in thefollowing empirical studies

Table 2 compares the forecasting performance in termsof the NMSE for the MLP EMD-MLP and EMD-MLPlowastmodels e NMSE is reported as the percentage for l-dayahead predictions where l 1 5 10 20 and 30 For eachprediction period the minimumNMSE is designated in boldfont Panel A of Table 2 displays the experimental results ofthe MLP models It is clear that with the increase inforecasting period the NMSE becomes larger suggestingreduced forecasting accuracy for a longer forecasting periodAlso the more complex MLPmodels with two hidden layers

MLP

Prediction

MLP MLPhellip

Time series data

EMD

c1(t) c2(t)

c2(t)

cn(t)

cn(t)

sum

rn(t)

rn(t)ˆ ˆ ˆ

Figure 3 An example of the EMD(-1)-MLPlowast model We de-compose a time series data by the EMD and generate n IMFcomponents c1(t) c2(t) cn(t) and one residue rn(t) Besidesc1(t) we forecast each decomposition and them sum them as theprediction

6 Complexity

do not offer better forecasting accuracy and are even worsefor 1-day ahead prediction

e empirical results of EMD-MLP are discussed inPanel B of Table 2 EMD(-1)-MLP treats the highest fre-quency IMF c1 as noise and applies the MLP model aftersubtracting the c1 series from the original time seriesEmpirical results show that the NMSE of 1-day aheadforecasting dropped dramatically however improvement of5-day ahead forecasting with EMD(-1)-MLP models islimited EMD(-2)-MLP models which deduct the twohighest frequency IMF series perform better than EMD(-1)-MLP models in the 5-day ahead forecasting experiment Inthe same way the EMD(-3)-MLP models perform betterwhen the forecasting period is longer than 10 days eresults of EMD-MLPlowast models are shown in Panel C ofTable 2 Although the calculation process is more compli-cated the forecasting performance of EMD-MLPlowast is alwaysbetter than MLP or EMD-MLP models according to the

criterion of NMSE In addition the random walk modelswith and without drifts (the random walk model withoutdrifts predicts that all future values will equal the last ob-served value Given a variable Y the k-step-ahead forecastfrom period t of Y is 1113954Yt+k Yt For the random walk modelwith drifts the k-step-ahead forecast from period t of Y is1113954Yt+k Yt + k1113954d where 1113954d is estimated by the average changeof Yt in the past 60 days) are used to examine the same datae related results in Panel D of Table 2 indicate that for theMLP-EMD and MLP-EMDlowast models their performance isobviously better than the random walk models in mostsituations

Table 3 is based on the forecasting performance of theabove models with Dstat which shows similar experimentalresults to the NMSE criterione table shows that if EMD(-2)-MLP(53)lowast is applied to forecasting the direction of theCNY series 30 days later the hitting rate can be as high as8639 In general although the calculation of EMD-MLPlowast

minus002500000025

c1

minus006minus003

000003006

c2

minus004

000

004

c3

minus003000003006

c4

minus004000004008

c5

minus005

000

005

c6

65707580

Resid

ual

0 1000 2000Time

6065707580

Raw

dat

a

Empirical mode decomposition

Figure 4 EMD decomposition of CNY from 2006 to 2015 is shown in this figure including the raw data series 6 IMFs and one residual

Complexity 7

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

c1

minus002000002

c2

minus0050minus0025

000000250050

c3

minus006minus003

000003006

c4

minus004000004008

c5

minus004000004008

c6

minus010minus005

000005010

c762636465

Resid

ual

0 500 1000Time

60

62

64

66

Raw

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a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 5: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

h11(t) x(t) minus m

11(t) (4)

If h11(t) does not meet the above two conditions this

study then takes h11(t) as a new data series and repeats

procedure (4) us we calculate

h12(t) h

11(t) minus m

12(t) (5)

In this calculation m12(t) is the mean value of the upper

and lower envelopes of h11(t)

Repeating the same procedure until meeting bothconditions we get the first IMF component of x(t) c1(t)that is

c1(t) h1q(t) (6)

e stopping rule indicates that absolute values of theenvelope meanmust be less than the user-specified tolerancelevel In this study the tolerance level is denoted as thestandard deviation of x(t) times 001 Other interestingstopping rules can be found in the works of Huang et al [26]and Huang and Wu [35]

After extracting the component c1(t) from x(t) wedenote another series r1(t) x(t) minus c1(t) which containsall information except c1(t) Huang et al [36] suggest asifting stop criterion that is rn(t) becomes a monotonicfunction or cannot extract more IMFs Finally the timeseries x(t) can be expressed as

x(t) 1113944n

i1ci(t) + rn(t) (7)

where n is the number of IMFs and rn(t) is the final residuewhich represents the central tendency of the data series x(t)ese IMFs are nearly orthogonal to each other and all havemeans of nearly zero According to the above properties it ispossible to forecast all decompositions and summarize theseestimations to predict x(t)

23 Overall Forecasting Process and Model NotationsConsidering the time series pt t 1 2 T we would liketo predict l-day ahead which is denoted as 1113954pt+l In this studythe input variables (past observations) include ptminus 59 ptminus 19ptminus 9 and ptminus 4 to pt which represent the past price levels of60 days 20 days 10 days and the last 5 days respectivelye output is the l-day ahead prediction Formally it couldbe shown as follows

1113954pt+l φ pt ptminus 4 ptminus 9 ptminus 19 ptminus 59w( 1113857 (8)

where φ(middot) is a function determined by neural networktraining and w is a weight vector of all parameters of MLP

ree kinds of forecasting models are adopted in thisstudy e first is the pure MLP model with one and twohidden layers e second is an EMD-MLP model whichuses EMD to subtract some volatile IMFs from the originaldata series and then uses the new data series to calculate thefinal prediction by MLP technology Figure 2 indicates theprocedure of the EMD(-1)-MLP model which means thefirst IMF component is ignored e third kind of model is

named EMD-MLPlowast which generally consists of the fol-lowing four steps

(1) Decompose the original time series into IMF com-ponents and one residual component via EMD

(2) Determine how many IMF components are usedwhich depends on the length of the forecastingperiod

(3) For each chosen IMF and residual component theMLP model is used as a forecasting tool to modelthese components and to make the correspondingprediction

(4) Add all prediction results to one value which can beseen as the final prediction result for the original timeseries

As an example Figure 3 represents the above procedureof the EMD(-1)-MLPlowast model Time series data aredecomposed via EMD and generates n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) In addition toc1(t) we forecast each decomposition and then sum them asthe prediction results for the original time series

3 Empirical Experiments

31 Data Two kinds of currency exchange rates of USD toRMB are considered in this study If the RMB is tradedonshore (in mainland China) it is referred to as CNY and iftraded offshore (mainly in Hong Kong) it is named CNH

MLP

Prediction

hellip

Time series data

EMD

New series data

c1(t) c2(t) cn(t) rn(t)

sum

Figure 2 An example of the EMD(-1)-MLPmodelWe decomposea time series data by the EMD and generate n IMF componentsc1(t) c2(t) cn(t) and one residue rn(t) We sum all de-compositions except c1(t) to produce a new time series data enthe MLP is applied to compute the prediction

Complexity 5

Both time series data are downloaded from Bloomberg ForCNY daily data from January 2 2006 to December 21 2015with a total of 2584 observations are examined in this studySince the CNH officially commenced on July 19 2010 itssample period is from January 3 2011 to December 21 2015with a total of 1304 observations For training the neuralnetwork models two-thirds of the observations are ran-domly assigned to the training dataset and the remainder isused as the testing dataset In addition it should be notedthat the time series in price levels is used in the followinganalysis rather than in return levels

According to descriptions shown in Section 32 theEMD technique is used to decompose both CNY and CNHprice series into several independent IMFs and one residualcomponent e decomposed results of CNY and CNH arerepresented in Figures 4 and 5 Comparing these two figuresthe original data series and decompositions seem dissimilarwhich is due to the different lengths of the sample periods Infact their IMFs have some similar characteristics Firstfocusing on the sample period 2011ndash2015 their residualcomponents have the same trend Starting at about 65 theydrop slightly to 62 and then rise slightly to 65 Second theswing period of high-frequency IMFs is shorter and also themean of absolute values of high-frequency IMFs is smallerwhen compared with low frequency For example in theseries of CNY the absolute values of c1 c3 and c5 are000298 000596 and 002002 respectively In our estima-tion model it is not necessary to include all the high-fre-quency IMFs as considering high-frequency IMFs may

reduce the forecasting accuracy when the forecasting periodis long erefore in the model EMD-MLP the high-fre-quency IMF is removed to get the denoised time series Inthe model EMD-MLPlowast not only are all the decompositionschosen to forecast the exchange rate but consideration isalso given to using part of the decompositions to conductforecasting discarding the high-frequency IMF series

32 Experimental Results Two main criteria are consideredin this empirical experiment the normalized mean squarederror (NMSE) and the directional statistic (Dstat) to eval-uate the levels of prediction and directional forecastingrespectively Typically following [37] the NMSE is definedby

NMSE 1σ2Ψ

1Nt

1113944sisinΨ

1113954ps+l minus ps+l( 11138572 (9)

where Ψ refers to the test dataset containing Nt observa-tions 1113954ps+l is the l-day ahead prediction ps+l is the actualvalue and σ2Ψ is the variance of ps+l Clearly the NMSE isone of the most important criteria for measuring the validityof the forecasting model but from a business perspectiveimproving the accuracy of directional predictions cansupport decision-making so as to generate greater profitsFurthermore the Diebold-Mariano (DM) test [38] isadopted to investigate whether adding EMD could improvethe forecasting performance of the MLP model Specificallythe null hypothesis is that the EMD-MLP (or EMD-MLPlowast)model has a lower forecast accuracy than the correspondingMLP model For example in the case of the EMD(-1)-MLP(53) the corresponding model infers the MLP(53)model

Besides the NMSE evaluation the directional statistic(Dstat) is applied to measure the ability to predict movementdirection [27 39] which can be expressed as

Dstat 1

Nt

1113944sisinΨ

as times 100 (10)

where as 1 if (1113954ps+l minus ps)(ps+l minus ps)ge 0 and as 0 other-wise Pesaran and Timmermann [40] provide the directionalaccuracy (DAC) test to examine predictive performance Inthis case the DAC test is used to determine whether Dstat issignificantly larger than 05 We have also adopted the excessprofitability test proposed by Anatolyev and Gerko [41] inevery related empirical study Since both tests produce thesame outcome we only report the results of DAC tests in thefollowing empirical studies

Table 2 compares the forecasting performance in termsof the NMSE for the MLP EMD-MLP and EMD-MLPlowastmodels e NMSE is reported as the percentage for l-dayahead predictions where l 1 5 10 20 and 30 For eachprediction period the minimumNMSE is designated in boldfont Panel A of Table 2 displays the experimental results ofthe MLP models It is clear that with the increase inforecasting period the NMSE becomes larger suggestingreduced forecasting accuracy for a longer forecasting periodAlso the more complex MLPmodels with two hidden layers

MLP

Prediction

MLP MLPhellip

Time series data

EMD

c1(t) c2(t)

c2(t)

cn(t)

cn(t)

sum

rn(t)

rn(t)ˆ ˆ ˆ

Figure 3 An example of the EMD(-1)-MLPlowast model We de-compose a time series data by the EMD and generate n IMFcomponents c1(t) c2(t) cn(t) and one residue rn(t) Besidesc1(t) we forecast each decomposition and them sum them as theprediction

6 Complexity

do not offer better forecasting accuracy and are even worsefor 1-day ahead prediction

e empirical results of EMD-MLP are discussed inPanel B of Table 2 EMD(-1)-MLP treats the highest fre-quency IMF c1 as noise and applies the MLP model aftersubtracting the c1 series from the original time seriesEmpirical results show that the NMSE of 1-day aheadforecasting dropped dramatically however improvement of5-day ahead forecasting with EMD(-1)-MLP models islimited EMD(-2)-MLP models which deduct the twohighest frequency IMF series perform better than EMD(-1)-MLP models in the 5-day ahead forecasting experiment Inthe same way the EMD(-3)-MLP models perform betterwhen the forecasting period is longer than 10 days eresults of EMD-MLPlowast models are shown in Panel C ofTable 2 Although the calculation process is more compli-cated the forecasting performance of EMD-MLPlowast is alwaysbetter than MLP or EMD-MLP models according to the

criterion of NMSE In addition the random walk modelswith and without drifts (the random walk model withoutdrifts predicts that all future values will equal the last ob-served value Given a variable Y the k-step-ahead forecastfrom period t of Y is 1113954Yt+k Yt For the random walk modelwith drifts the k-step-ahead forecast from period t of Y is1113954Yt+k Yt + k1113954d where 1113954d is estimated by the average changeof Yt in the past 60 days) are used to examine the same datae related results in Panel D of Table 2 indicate that for theMLP-EMD and MLP-EMDlowast models their performance isobviously better than the random walk models in mostsituations

Table 3 is based on the forecasting performance of theabove models with Dstat which shows similar experimentalresults to the NMSE criterione table shows that if EMD(-2)-MLP(53)lowast is applied to forecasting the direction of theCNY series 30 days later the hitting rate can be as high as8639 In general although the calculation of EMD-MLPlowast

minus002500000025

c1

minus006minus003

000003006

c2

minus004

000

004

c3

minus003000003006

c4

minus004000004008

c5

minus005

000

005

c6

65707580

Resid

ual

0 1000 2000Time

6065707580

Raw

dat

a

Empirical mode decomposition

Figure 4 EMD decomposition of CNY from 2006 to 2015 is shown in this figure including the raw data series 6 IMFs and one residual

Complexity 7

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

c1

minus002000002

c2

minus0050minus0025

000000250050

c3

minus006minus003

000003006

c4

minus004000004008

c5

minus004000004008

c6

minus010minus005

000005010

c762636465

Resid

ual

0 500 1000Time

60

62

64

66

Raw

dat

a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 6: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

Both time series data are downloaded from Bloomberg ForCNY daily data from January 2 2006 to December 21 2015with a total of 2584 observations are examined in this studySince the CNH officially commenced on July 19 2010 itssample period is from January 3 2011 to December 21 2015with a total of 1304 observations For training the neuralnetwork models two-thirds of the observations are ran-domly assigned to the training dataset and the remainder isused as the testing dataset In addition it should be notedthat the time series in price levels is used in the followinganalysis rather than in return levels

According to descriptions shown in Section 32 theEMD technique is used to decompose both CNY and CNHprice series into several independent IMFs and one residualcomponent e decomposed results of CNY and CNH arerepresented in Figures 4 and 5 Comparing these two figuresthe original data series and decompositions seem dissimilarwhich is due to the different lengths of the sample periods Infact their IMFs have some similar characteristics Firstfocusing on the sample period 2011ndash2015 their residualcomponents have the same trend Starting at about 65 theydrop slightly to 62 and then rise slightly to 65 Second theswing period of high-frequency IMFs is shorter and also themean of absolute values of high-frequency IMFs is smallerwhen compared with low frequency For example in theseries of CNY the absolute values of c1 c3 and c5 are000298 000596 and 002002 respectively In our estima-tion model it is not necessary to include all the high-fre-quency IMFs as considering high-frequency IMFs may

reduce the forecasting accuracy when the forecasting periodis long erefore in the model EMD-MLP the high-fre-quency IMF is removed to get the denoised time series Inthe model EMD-MLPlowast not only are all the decompositionschosen to forecast the exchange rate but consideration isalso given to using part of the decompositions to conductforecasting discarding the high-frequency IMF series

32 Experimental Results Two main criteria are consideredin this empirical experiment the normalized mean squarederror (NMSE) and the directional statistic (Dstat) to eval-uate the levels of prediction and directional forecastingrespectively Typically following [37] the NMSE is definedby

NMSE 1σ2Ψ

1Nt

1113944sisinΨ

1113954ps+l minus ps+l( 11138572 (9)

where Ψ refers to the test dataset containing Nt observa-tions 1113954ps+l is the l-day ahead prediction ps+l is the actualvalue and σ2Ψ is the variance of ps+l Clearly the NMSE isone of the most important criteria for measuring the validityof the forecasting model but from a business perspectiveimproving the accuracy of directional predictions cansupport decision-making so as to generate greater profitsFurthermore the Diebold-Mariano (DM) test [38] isadopted to investigate whether adding EMD could improvethe forecasting performance of the MLP model Specificallythe null hypothesis is that the EMD-MLP (or EMD-MLPlowast)model has a lower forecast accuracy than the correspondingMLP model For example in the case of the EMD(-1)-MLP(53) the corresponding model infers the MLP(53)model

Besides the NMSE evaluation the directional statistic(Dstat) is applied to measure the ability to predict movementdirection [27 39] which can be expressed as

Dstat 1

Nt

1113944sisinΨ

as times 100 (10)

where as 1 if (1113954ps+l minus ps)(ps+l minus ps)ge 0 and as 0 other-wise Pesaran and Timmermann [40] provide the directionalaccuracy (DAC) test to examine predictive performance Inthis case the DAC test is used to determine whether Dstat issignificantly larger than 05 We have also adopted the excessprofitability test proposed by Anatolyev and Gerko [41] inevery related empirical study Since both tests produce thesame outcome we only report the results of DAC tests in thefollowing empirical studies

Table 2 compares the forecasting performance in termsof the NMSE for the MLP EMD-MLP and EMD-MLPlowastmodels e NMSE is reported as the percentage for l-dayahead predictions where l 1 5 10 20 and 30 For eachprediction period the minimumNMSE is designated in boldfont Panel A of Table 2 displays the experimental results ofthe MLP models It is clear that with the increase inforecasting period the NMSE becomes larger suggestingreduced forecasting accuracy for a longer forecasting periodAlso the more complex MLPmodels with two hidden layers

MLP

Prediction

MLP MLPhellip

Time series data

EMD

c1(t) c2(t)

c2(t)

cn(t)

cn(t)

sum

rn(t)

rn(t)ˆ ˆ ˆ

Figure 3 An example of the EMD(-1)-MLPlowast model We de-compose a time series data by the EMD and generate n IMFcomponents c1(t) c2(t) cn(t) and one residue rn(t) Besidesc1(t) we forecast each decomposition and them sum them as theprediction

6 Complexity

do not offer better forecasting accuracy and are even worsefor 1-day ahead prediction

e empirical results of EMD-MLP are discussed inPanel B of Table 2 EMD(-1)-MLP treats the highest fre-quency IMF c1 as noise and applies the MLP model aftersubtracting the c1 series from the original time seriesEmpirical results show that the NMSE of 1-day aheadforecasting dropped dramatically however improvement of5-day ahead forecasting with EMD(-1)-MLP models islimited EMD(-2)-MLP models which deduct the twohighest frequency IMF series perform better than EMD(-1)-MLP models in the 5-day ahead forecasting experiment Inthe same way the EMD(-3)-MLP models perform betterwhen the forecasting period is longer than 10 days eresults of EMD-MLPlowast models are shown in Panel C ofTable 2 Although the calculation process is more compli-cated the forecasting performance of EMD-MLPlowast is alwaysbetter than MLP or EMD-MLP models according to the

criterion of NMSE In addition the random walk modelswith and without drifts (the random walk model withoutdrifts predicts that all future values will equal the last ob-served value Given a variable Y the k-step-ahead forecastfrom period t of Y is 1113954Yt+k Yt For the random walk modelwith drifts the k-step-ahead forecast from period t of Y is1113954Yt+k Yt + k1113954d where 1113954d is estimated by the average changeof Yt in the past 60 days) are used to examine the same datae related results in Panel D of Table 2 indicate that for theMLP-EMD and MLP-EMDlowast models their performance isobviously better than the random walk models in mostsituations

Table 3 is based on the forecasting performance of theabove models with Dstat which shows similar experimentalresults to the NMSE criterione table shows that if EMD(-2)-MLP(53)lowast is applied to forecasting the direction of theCNY series 30 days later the hitting rate can be as high as8639 In general although the calculation of EMD-MLPlowast

minus002500000025

c1

minus006minus003

000003006

c2

minus004

000

004

c3

minus003000003006

c4

minus004000004008

c5

minus005

000

005

c6

65707580

Resid

ual

0 1000 2000Time

6065707580

Raw

dat

a

Empirical mode decomposition

Figure 4 EMD decomposition of CNY from 2006 to 2015 is shown in this figure including the raw data series 6 IMFs and one residual

Complexity 7

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

c1

minus002000002

c2

minus0050minus0025

000000250050

c3

minus006minus003

000003006

c4

minus004000004008

c5

minus004000004008

c6

minus010minus005

000005010

c762636465

Resid

ual

0 500 1000Time

60

62

64

66

Raw

dat

a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 7: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

do not offer better forecasting accuracy and are even worsefor 1-day ahead prediction

e empirical results of EMD-MLP are discussed inPanel B of Table 2 EMD(-1)-MLP treats the highest fre-quency IMF c1 as noise and applies the MLP model aftersubtracting the c1 series from the original time seriesEmpirical results show that the NMSE of 1-day aheadforecasting dropped dramatically however improvement of5-day ahead forecasting with EMD(-1)-MLP models islimited EMD(-2)-MLP models which deduct the twohighest frequency IMF series perform better than EMD(-1)-MLP models in the 5-day ahead forecasting experiment Inthe same way the EMD(-3)-MLP models perform betterwhen the forecasting period is longer than 10 days eresults of EMD-MLPlowast models are shown in Panel C ofTable 2 Although the calculation process is more compli-cated the forecasting performance of EMD-MLPlowast is alwaysbetter than MLP or EMD-MLP models according to the

criterion of NMSE In addition the random walk modelswith and without drifts (the random walk model withoutdrifts predicts that all future values will equal the last ob-served value Given a variable Y the k-step-ahead forecastfrom period t of Y is 1113954Yt+k Yt For the random walk modelwith drifts the k-step-ahead forecast from period t of Y is1113954Yt+k Yt + k1113954d where 1113954d is estimated by the average changeof Yt in the past 60 days) are used to examine the same datae related results in Panel D of Table 2 indicate that for theMLP-EMD and MLP-EMDlowast models their performance isobviously better than the random walk models in mostsituations

Table 3 is based on the forecasting performance of theabove models with Dstat which shows similar experimentalresults to the NMSE criterione table shows that if EMD(-2)-MLP(53)lowast is applied to forecasting the direction of theCNY series 30 days later the hitting rate can be as high as8639 In general although the calculation of EMD-MLPlowast

minus002500000025

c1

minus006minus003

000003006

c2

minus004

000

004

c3

minus003000003006

c4

minus004000004008

c5

minus005

000

005

c6

65707580

Resid

ual

0 1000 2000Time

6065707580

Raw

dat

a

Empirical mode decomposition

Figure 4 EMD decomposition of CNY from 2006 to 2015 is shown in this figure including the raw data series 6 IMFs and one residual

Complexity 7

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

c1

minus002000002

c2

minus0050minus0025

000000250050

c3

minus006minus003

000003006

c4

minus004000004008

c5

minus004000004008

c6

minus010minus005

000005010

c762636465

Resid

ual

0 500 1000Time

60

62

64

66

Raw

dat

a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

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Page 8: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

models is more complicated the forecasting ability appearsto be the best of all the proposed models e highest fre-quency IMF is therefore treated as noise and EMD(-1)-MLPlowast is used for the forecast In this way the performanceof the selected model would be relatively better based onboth NMSE and Dstat criteria Besides it should be notedthat performance of predicting over longer periods is worsethan shorter ones intuitively In terms of NMSE the ex-perimental results are consistent with above argument iethe NMSE performance of predicting 20 and 30-days aheadis poor But the Dstat performance is totally different ourresults show that predictions over longer periods often havehigher Dstat (in order to verify the robustness we also used

three-fourths of the observations as a training dataset toreexamine the results of Tables 2 and 3e related outcomesare shown in Tables 4 and 5 In addition we considered ahyperbolic tangent function as the activation function andreported related results in Tables 6 and 7)

In addition to the above experiments the dataset of CNYand CNH series from 2011 to 2015 is considered We use thesame method of dividing the data into the training set andtesting set According to the experimental results in Tables 2and 3 we do not report MLP models and only adopt anumber of EMD-MLP and EMD-MLPlowast models to conductpredictions e statistical results of NMSE and Dstat areshown in Tables 8 and 9 respectively

minus006minus003

000003006

c1

minus002000002

c2

minus0050minus0025

000000250050

c3

minus006minus003

000003006

c4

minus004000004008

c5

minus004000004008

c6

minus010minus005

000005010

c762636465

Resid

ual

0 500 1000Time

60

62

64

66

Raw

dat

a

Empirical mode decomposition

Figure 5 EMD decomposition of CNH from 2011 to 2015 is shown in this figure including the raw data series 7 IMFs and one residual

8 Complexity

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 9: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

Tables 8 and 9 indicate the EMD-MLPlowast models performbetter than the EMD-MLP models on both NMSE and Dstatcriteria Comparing the results of the CNY and CNH seriesthe NMSE of CNY is found to be less than that of CNH on

average no matter how long the forecasting period emain reason for this is the original volatility of CNY series issmaller than that of CNH series For the Dstat test partforecasting performance improves with the growth of

Table 2 NMSE comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00231 00874 02118 03698 05888MLP(5) 00204 00854 02088 03939 05723MLP(53) 00285 00943 02088 03623 04746MLP(64) 00376 00896 02021 03613 05453Panel B EMD-MLP modelEMD(-1)-MLP(3) 00145⋆⋆⋆ 00823 02120 03894 05217⋆EMD(-1)-MLP(53) 00143⋆⋆⋆ 00821⋆⋆ 02111 03836 05447EMD(-2)-MLP(3) 00207 00450⋆⋆⋆ 01613⋆⋆ 03760 05258EMD(-2)-MLP(53) 00236⋆⋆ 00505⋆⋆⋆ 01583⋆⋆ 03667 05258EMD(-3)-MLP(3) 00434 00436⋆⋆⋆ 00739⋆⋆ 02162⋆⋆ 04355⋆⋆⋆EMD(-3)-MLP(53) 00419 00456⋆⋆⋆ 00694⋆⋆ 02144⋆⋆ 03892⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00087⋆⋆⋆ 00217⋆⋆⋆ 00410⋆⋆⋆ 00806⋆⋆⋆ 01244⋆⋆⋆EMD(0)-MLP(53)lowast 00088⋆⋆⋆ 00222⋆⋆⋆ 00404⋆⋆⋆ 00695⋆⋆⋆ 01048⋆⋆⋆EMD(-1)-MLP(3)lowast 00075⋆⋆⋆ 00200⋆⋆⋆ 00385⋆⋆⋆ 00812⋆⋆⋆ 01136⋆⋆⋆EMD(-1)-MLP(53)lowast 00083⋆⋆⋆ 00314⋆⋆⋆ 00368⋆⋆⋆ 00681⋆⋆⋆ 01051⋆⋆⋆EMD(-2)-MLP(3)lowast 00172⋆ 00214⋆⋆⋆ 00444⋆⋆⋆ 00760⋆⋆⋆ 01152⋆⋆⋆EMD(-2)-MLP(53)lowast 00190⋆⋆ 00256⋆⋆⋆ 00423⋆⋆⋆ 00759⋆⋆⋆ 01034⋆⋆⋆

Panel D random walk modelNo drift 00144 00861 02349 05323 09357With drift 00148 00973 02834 06981 12954Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms ofthe NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 3 Dstat comparisons for different models

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5174 5349 6349⋆⋆⋆ 6965⋆⋆⋆ 7072⋆⋆⋆MLP(5) 5198 5517 6217⋆⋆⋆ 6844⋆⋆⋆ 7108⋆⋆⋆MLP(53) 5018 5493 6578⋆⋆⋆ 6929⋆⋆⋆ 7339⋆⋆⋆MLP(64) 4898 5541 6265⋆⋆⋆ 6989⋆⋆⋆ 7120⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6194⋆⋆⋆ 5974⋆⋆⋆ 6699⋆⋆⋆ 6904⋆⋆⋆ 7254⋆⋆⋆EMD(-1)-MLP(53) 6242⋆⋆⋆ 5769⋆⋆⋆ 6554⋆⋆⋆ 6892⋆⋆⋆ 7132⋆⋆⋆EMD(-2)-MLP(3) 6230⋆⋆⋆ 6947⋆⋆⋆ 6964⋆⋆⋆ 6941⋆⋆⋆ 7242⋆⋆⋆EMD(-2)-MLP(53) 6002⋆⋆⋆ 6671⋆⋆⋆ 7024⋆⋆⋆ 7025⋆⋆⋆ 7254⋆⋆⋆EMD(-3)-MLP(3) 5750⋆⋆⋆ 7296⋆⋆⋆ 7867⋆⋆⋆ 7533⋆⋆⋆ 7363⋆⋆⋆EMD(-3)-MLP(53) 5678⋆⋆⋆ 6959⋆⋆⋆ 8048⋆⋆⋆ 7437⋆⋆⋆ 7327⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6999⋆⋆⋆ 8065⋆⋆⋆ 8145⋆⋆⋆ 8259⋆⋆⋆ 8639⋆⋆⋆EMD(0)-MLP(53)lowast 6831⋆⋆⋆ 7945⋆⋆⋆ 8036⋆⋆⋆ 8295⋆⋆⋆ 8578⋆⋆⋆EMD(-1)-MLP(3)lowast 7167⋆⋆⋆ 8101⋆⋆⋆ 8108⋆⋆⋆ 8186⋆⋆⋆ 8408⋆⋆⋆EMD(-1)-MLP(53)lowast 7035⋆⋆⋆ 8017⋆⋆⋆ 8289⋆⋆⋆ 8295⋆⋆⋆ 8639⋆⋆⋆EMD(-2)-MLP(3)lowast 6351⋆⋆⋆ 8089⋆⋆⋆ 8072⋆⋆⋆ 8210⋆⋆⋆ 8615⋆⋆⋆EMD(-2)-MLP(53)lowast 6351⋆⋆⋆ 7873⋆⋆⋆ 8241⋆⋆⋆ 8198⋆⋆⋆ 8639⋆⋆⋆

Consider CNY from January 2 2006 to December 21 2015 with a total of 2584 observationsis table compares the forecasting performance in terms of theDstat for theMLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover weexamine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10respectively For each length of prediction we mark the maximum Dstat as bold

Complexity 9

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 10: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

forecasting periods Also no significant difference is foundfor the results of CNY and CNH series based onDstat criteriaFor forecasting over 20 days ahead the hitting rate exceeds89 Even for forecasting 1-day ahead Dstat can achievemore than 79

33 Applying the Trading Strategy is part introduces anapplication for designing a trading strategy for CNY (sincethe cases of CNY and CNH from 2011 to 2015 produce thesimilar results we do not report the latter in this paper)According to the results in Tables 2 and 3 in terms of NMSE

Table 4 Robust tests for NMSE comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00175 00740 02010 03638 05954MLP(5) 00201 00699 02082 03663 05158MLP(53) 00212 00761 02117 03614 05561MLP(64) 00221 00694 02066 03586 05746Panel B EMD-MLP modelEMD(-1)-MLP(3) 00137⋆⋆⋆ 00705 01444⋆⋆ 03827 05885EMD(-1)-MLP(53) 00117⋆⋆⋆ 00713 01982⋆⋆⋆ 03251⋆⋆ 04948⋆⋆⋆EMD(-2)-MLP(3) 00192 00371⋆⋆⋆ 01434⋆⋆ 03568 05725⋆EMD(-2)-MLP(53) 00222 00380⋆⋆⋆ 01433⋆⋆ 03380⋆ 05417EMD(-3)-MLP(3) 00423 00468⋆⋆⋆ 00691⋆⋆⋆ 02003⋆⋆ 04676⋆⋆EMD(-3)-MLP(53) 00442 00410⋆⋆⋆ 00647⋆⋆⋆ 01965⋆⋆ 04551⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00079⋆⋆⋆ 00201⋆⋆⋆ 00391⋆⋆⋆ 00798⋆⋆⋆ 01302⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00213⋆⋆⋆ 00461⋆⋆⋆ 00614⋆⋆⋆ 01160⋆⋆⋆EMD(-1)-MLP(3)lowast 00083⋆⋆⋆ 00192⋆⋆⋆ 00413⋆⋆⋆ 00717⋆⋆⋆ 01298⋆⋆⋆EMD(-1)-MLP(53)lowast 00091⋆⋆⋆ 00220⋆⋆⋆ 00425⋆⋆⋆ 00655⋆⋆⋆ 01140⋆⋆⋆EMD(-2)-MLP(3)lowast 00191 00222⋆⋆⋆ 00456⋆⋆⋆ 00801⋆⋆⋆ 01294⋆⋆⋆EMD(-2)-MLP(53)lowast 00201 00240⋆⋆⋆ 00381⋆⋆⋆ 00660⋆⋆⋆ 01050⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We report the NMSE as percentage for l-day ahead predictions where l

1 5 10 20 and 30e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLPmodel ⋆⋆⋆ ⋆⋆and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 5 Robust tests for Dstat comparisons with different subsamples

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 4976 5698 6343⋆⋆⋆ 7013⋆⋆⋆ 7115⋆⋆⋆MLP(5) 4596 5698 6661⋆⋆⋆ 6981⋆⋆⋆ 7212⋆⋆⋆MLP(53) 5388⋆⋆ 5556 6407⋆⋆⋆ 6949⋆⋆⋆ 7067⋆⋆⋆MLP(64) 4992 5968⋆⋆ 6312⋆⋆⋆ 6885⋆⋆⋆ 7147⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6212⋆⋆⋆ 5714⋆ 7154⋆⋆⋆ 6917⋆⋆⋆ 7179⋆⋆⋆EMD(-1)-MLP(53) 6276⋆⋆⋆ 5698 6725⋆⋆⋆ 7093⋆⋆⋆ 7404⋆⋆⋆EMD(-2)-MLP(3) 6403⋆⋆⋆ 7159⋆⋆⋆ 7218⋆⋆⋆ 6805⋆⋆⋆ 7099⋆⋆⋆EMD(-2)-MLP(53) 6292⋆⋆⋆ 7270⋆⋆⋆ 7202⋆⋆⋆ 6997⋆⋆⋆ 7212⋆⋆⋆EMD(-3)-MLP(3) 5594⋆⋆⋆ 7016⋆⋆⋆ 7901⋆⋆⋆ 7588⋆⋆⋆ 7436⋆⋆⋆EMD(-3)-MLP(53) 5563⋆⋆⋆ 7524⋆⋆⋆ 8060⋆⋆⋆ 7604⋆⋆⋆ 7308⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 6989⋆⋆⋆ 7937⋆⋆⋆ 8108⋆⋆⋆ 8035⋆⋆⋆ 8686⋆⋆⋆EMD(0)-MLP(53)lowast 7211⋆⋆⋆ 8254⋆⋆⋆ 8060⋆⋆⋆ 8243⋆⋆⋆ 8638⋆⋆⋆EMD(-1)-MLP(3)lowast 6783⋆⋆⋆ 8190⋆⋆⋆ 8140⋆⋆⋆ 8131⋆⋆⋆ 8750⋆⋆⋆EMD(-1)-MLP(53)lowast 6846⋆⋆⋆ 8159⋆⋆⋆ 8219⋆⋆⋆ 8067⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(3)lowast 6181⋆⋆⋆ 8063⋆⋆⋆ 8124⋆⋆⋆ 8035⋆⋆⋆ 8718⋆⋆⋆EMD(-2)-MLP(53)lowast 6323⋆⋆⋆ 8032⋆⋆⋆ 8283⋆⋆⋆ 8147⋆⋆⋆ 8670⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations For training the neural network models three-fourths of theobservations are randomly assigned to the training dataset and the remainder is used as the testing dataset is table compares the forecasting performancein terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

10 Complexity

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 11: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

and Dstat the best model for predicting l-day ahead can bedetermined e forecasting model can be trained based onpast exchange rate series and produce l-day ahead pre-dictions According to the forecasting results tradingstrategies are set as follows

long if 1113954ps+l gtps times(1 + τ)

short if 1113954ps+l ltps times(1 minus τ)(11)

where 1113954ps+l is the l-day ahead predictions at time s and τ is acritical number We long (short) the CNY if l-day ahead

Table 6 Robust tests for NMSE comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 00281 00877 02123 03729 05579MLP(5) 00245 00820 02075 03729 05149MLP(53) 00260 00859 02079 03491 04450MLP(64) 00222 00887 01996 03436 04733Panel B EMD-MLP modelEMD(-1)-MLP(3) 00120⋆⋆⋆ 00830 02045 03717 05285EMD(-1)-MLP(53) 00137⋆⋆⋆ 00862 02097 03662 05282EMD(-2)-MLP(3) 00204⋆⋆ 00354⋆⋆⋆ 01466⋆⋆⋆ 03654 05571EMD(-2)-MLP(53) 00182⋆⋆ 00351⋆⋆⋆ 01636⋆⋆ 03665 04772EMD(-3)-MLP(3) 00417 00450⋆⋆⋆ 00705⋆⋆⋆ 02140⋆⋆ 05782EMD(-3)-MLP(53) 00393 00441⋆⋆⋆ 00711⋆⋆⋆ 02198⋆⋆ 03996Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 00077⋆⋆⋆ 00226⋆⋆⋆ 00491⋆⋆⋆ 00820⋆⋆⋆ 01246⋆⋆⋆EMD(0)-MLP(53)lowast 00084⋆⋆⋆ 00198⋆⋆⋆ 00382⋆⋆⋆ 00669⋆⋆⋆ 01106⋆⋆⋆EMD(-1)-MLP(3)lowast 00095⋆⋆⋆ 00223⋆⋆⋆ 00482⋆⋆⋆ 00826⋆⋆⋆ 01528⋆⋆⋆EMD(-1)-MLP(53)lowast 00084⋆⋆⋆ 00258⋆⋆⋆ 00460⋆⋆⋆ 00845⋆⋆⋆ 01210⋆⋆⋆EMD(-2)-MLP(3)lowast 00212⋆⋆ 00239⋆⋆⋆ 00469⋆⋆⋆ 00892⋆⋆⋆ 01316⋆⋆⋆EMD(-2)-MLP(53)lowast 00196⋆⋆ 00229⋆⋆⋆ 00414⋆⋆⋆ 00784⋆⋆⋆ 01497⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of the NMSE for the MLP EMD-MLP and EMD-MLPlowast models We reportthe NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and 30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP(EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length ofprediction we mark the minimum NMSE as bold

Table 7 Robust tests for Dstat comparisons with different activation functions

1-day 5-day 10-day 20-day 30-dayPanel A MLP modelMLP(3) 5006 5517 6241⋆⋆⋆ 6856⋆⋆⋆ 7181⋆⋆⋆MLP(5) 4898 5685⋆ 6325⋆⋆⋆ 6917⋆⋆⋆ 7254⋆⋆⋆MLP(53) 4814 5481 6530⋆⋆⋆ 6699⋆⋆⋆ 7217⋆⋆⋆MLP(64) 4994 5625⋆⋆ 6145⋆⋆⋆ 6868⋆⋆⋆ 7242⋆⋆⋆

Panel B EMD-MLP modelEMD(-1)-MLP(3) 6999⋆⋆⋆ 5841⋆⋆⋆ 6795⋆⋆⋆ 7001⋆⋆⋆ 7145⋆⋆⋆EMD(-1)-MLP(53) 6795⋆⋆⋆ 5781⋆⋆⋆ 6446⋆⋆⋆ 7025⋆⋆⋆ 7339⋆⋆⋆EMD(-2)-MLP(3) 6459⋆⋆⋆ 7320⋆⋆⋆ 7036⋆⋆⋆ 7037⋆⋆⋆ 7108⋆⋆⋆EMD(-2)-MLP(53) 6351⋆⋆⋆ 7584⋆⋆⋆ 6940⋆⋆⋆ 6989⋆⋆⋆ 7400⋆⋆⋆EMD(-3)-MLP(3) 5726⋆⋆⋆ 7248⋆⋆⋆ 7880⋆⋆⋆ 7521⋆⋆⋆ 6889⋆⋆⋆EMD(-3)-MLP(53) 5738⋆⋆⋆ 7188⋆⋆⋆ 8000⋆⋆⋆ 7340⋆⋆⋆ 7339⋆⋆⋆

Panel C EMD-MLPlowast modelEMD(0)-MLP(3)lowast 7107⋆⋆⋆ 7897⋆⋆⋆ 8096⋆⋆⋆ 8271⋆⋆⋆ 8676⋆⋆⋆EMD(0)-MLP(53)lowast 7203⋆⋆⋆ 7885⋆⋆⋆ 8036⋆⋆⋆ 8210⋆⋆⋆ 8748⋆⋆⋆EMD(-1)-MLP(3)lowast 6819⋆⋆⋆ 7752⋆⋆⋆ 8072⋆⋆⋆ 8162⋆⋆⋆ 8481⋆⋆⋆EMD(-1)-MLP(53)lowast 7011⋆⋆⋆ 7728⋆⋆⋆ 8012⋆⋆⋆ 8307⋆⋆⋆ 8603⋆⋆⋆EMD(-2)-MLP(3)lowast 6182⋆⋆⋆ 7897⋆⋆⋆ 8108⋆⋆⋆ 8077⋆⋆⋆ 8518⋆⋆⋆EMD(-2)-MLP(53)lowast 6471⋆⋆⋆ 7885⋆⋆⋆ 7880⋆⋆⋆ 8259⋆⋆⋆ 8335⋆⋆⋆

Consider the CNY from January 2 2006 to December 21 2015 with a total of 2584 observations In this table a hyperbolic tangent function is used as theactivation function is table compares the forecasting performance in terms of Dstat for the MLP EMD-MLP and EMD-MLPlowast models We report Dstat aspercentage for l-day ahead predictions where l 1 5 10 20 and 30 Moreover we examine the ability of all models to predict the direction of change by theDAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5 and 10 respectively For each length of prediction wemark themaximumDstat as bold

Complexity 11

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 12: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

predictions are greater (smaller) than the present pricemultiplied by 1 + τ So unless 1113954ps+l ps(1 + τ) people al-ways conduct a transaction at time s and hold it for l daysFor instance consider the case with l 10 and τ 0 If ps

5 and we use the EMD-MLP model to find 1113954ps+l 52 we

immediately long CNY and hold it for 10 days On thecontrary if ps 5 and 1113954ps+l 49 we short it

e reason of setup τ comes from the following severalaspects first when we set τ 0 the number of transactionsmust be very large Since high frequency trading comes with

Table 8 NMSE comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 02078⋆ 07330⋆⋆⋆ 49711 114496 148922EMD(-2)-MLP(53) 03417 06292⋆⋆⋆ 27752⋆⋆ 84836 85811EMD(-3)-MLP(53) 06015 06098⋆⋆⋆ 12525⋆⋆⋆ 39844⋆⋆⋆ 72250EMD(0)-MLP(3)lowast 02171⋆ 04204⋆⋆⋆ 06304⋆⋆⋆ 16314⋆⋆⋆ 21985⋆⋆⋆EMD(0)-MLP(53)lowast 01711⋆⋆ 04124⋆⋆⋆ 06912⋆⋆⋆ 15200⋆⋆⋆ 16964⋆⋆⋆EMD(-1)-MLP(3)lowast 01497⋆⋆ 03928⋆⋆⋆ 07120⋆⋆⋆ 18627⋆⋆⋆ 21755⋆⋆⋆EMD(-1)-MLP(53)lowast 01610⋆ 04774⋆⋆⋆ 05999⋆⋆⋆ 12579⋆⋆⋆ 15669⋆⋆⋆EMD(-2)-MLP(3)lowast 02847 04485⋆⋆⋆ 08156⋆⋆⋆ 13609⋆⋆⋆ 19762⋆⋆⋆EMD(-2)-MLP(53)lowast 02960 04846⋆⋆⋆ 08578⋆⋆⋆ 12355⋆⋆⋆ 14642⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 03814⋆⋆⋆ 22893 64050 128439 209652EMD(-2)-MLP(53) 04732⋆⋆ 11208⋆⋆ 47997⋆ 122240 229451EMD(-3)-MLP(53) 09658 09270⋆⋆⋆ 23329⋆⋆⋆ 76194⋆⋆ 194264EMD(0)-MLP(3)lowast 02317⋆⋆⋆ 08170⋆⋆⋆ 12729⋆⋆⋆ 25680⋆⋆ 35197⋆⋆⋆EMD(0)-MLP(53)lowast 02600⋆⋆⋆ 06797⋆⋆⋆ 13611⋆⋆⋆ 24448⋆⋆ 32915⋆⋆EMD(-1)-MLP(3)lowast 02699⋆⋆⋆ 06471⋆⋆⋆ 14162⋆⋆⋆ 22991⋆⋆⋆ 38647⋆⋆⋆EMD(-1)-MLP(53)lowast 02379⋆⋆⋆ 07165⋆⋆⋆ 13509⋆⋆⋆ 23486⋆⋆ 30931⋆⋆EMD(-2)-MLP(3)lowast 04297⋆ 06346⋆⋆⋆ 12586⋆⋆⋆ 24497⋆⋆ 44241⋆⋆⋆EMD(-2)-MLP(53)lowast 04173⋆⋆ 07528⋆⋆⋆ 11915⋆⋆⋆ 25860⋆⋆ 31497⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of the NMSE for several forecasting models We report the NMSE as percentage for l-day ahead predictions where l 1 5 10 20 and30 e DM test [38] is used to compare the forecast accuracy of EMD-MLP (EMD-MLPlowast) model and the corresponding MLP model ⋆⋆⋆ ⋆⋆ and ⋆ denotestatistical significance at 1 5 and 10 respectively For each length of prediction we mark the minimum NMSE as bold

Table 9 Dstat comparisons for CNY and CNH

1-day 5-day 10-day 20-day 30-dayPanel A CNYEMD(-1)-MLP(53) 7365⋆⋆⋆ 7500⋆⋆⋆ 6427⋆⋆⋆ 6090⋆⋆⋆ 6490⋆⋆⋆EMD(-2)-MLP(53) 6749⋆⋆⋆ 7797⋆⋆⋆ 6923⋆⋆⋆ 6867⋆⋆⋆ 7778⋆⋆⋆EMD(-3)-MLP(53) 6182⋆⋆⋆ 7871⋆⋆⋆ 8313⋆⋆⋆ 7744⋆⋆⋆ 7828⋆⋆⋆EMD(0)-MLP(3)lowast 7537⋆⋆⋆ 7970⋆⋆⋆ 8362⋆⋆⋆ 8622⋆⋆⋆ 8460⋆⋆⋆EMD(0)-MLP(53)lowast 8005⋆⋆⋆ 8243⋆⋆⋆ 8486⋆⋆⋆ 8947⋆⋆⋆ 8813⋆⋆⋆EMD(-1)-MLP(3)lowast 7512⋆⋆⋆ 8317⋆⋆⋆ 8437⋆⋆⋆ 8722⋆⋆⋆ 8409⋆⋆⋆EMD(-1)-MLP(53)lowast 7488⋆⋆⋆ 8342⋆⋆⋆ 8536⋆⋆⋆ 8872⋆⋆⋆ 8611⋆⋆⋆EMD(-2)-MLP(3)lowast 6847⋆⋆⋆ 8243⋆⋆⋆ 8288⋆⋆⋆ 8872⋆⋆⋆ 8359⋆⋆⋆EMD(-2)-MLP(53)lowast 6970⋆⋆⋆ 8267⋆⋆⋆ 8337⋆⋆⋆ 8697⋆⋆⋆ 8788⋆⋆⋆

Panel B CNHEMD(-1)-MLP(53) 7324⋆⋆⋆ 6210⋆⋆⋆ 6250⋆⋆⋆ 6238⋆⋆⋆ 6584⋆⋆⋆EMD(-2)-MLP(53) 7032⋆⋆⋆ 7628⋆⋆⋆ 6667⋆⋆⋆ 6337⋆⋆⋆ 6484⋆⋆⋆EMD(-3)-MLP(53) 6107⋆⋆⋆ 7946⋆⋆⋆ 7892⋆⋆⋆ 7500⋆⋆⋆ 7531⋆⋆⋆EMD(0)-MLP(3)lowast 7981⋆⋆⋆ 8264⋆⋆⋆ 8407⋆⋆⋆ 8465⋆⋆⋆ 8903⋆⋆⋆EMD(0)-MLP(53)lowast 7664⋆⋆⋆ 8313⋆⋆⋆ 8309⋆⋆⋆ 8540⋆⋆⋆ 8978⋆⋆⋆EMD(-1)-MLP(3)lowast 7664⋆⋆⋆ 8215⋆⋆⋆ 8480⋆⋆⋆ 8465⋆⋆⋆ 8479⋆⋆⋆EMD(-1)-MLP(53)lowast 7883⋆⋆⋆ 8337⋆⋆⋆ 8505⋆⋆⋆ 8465⋆⋆⋆ 8953⋆⋆⋆EMD(-2)-MLP(3)lowast 7153⋆⋆⋆ 8386⋆⋆⋆ 8431⋆⋆⋆ 8787⋆⋆⋆ 8529⋆⋆⋆EMD(-2)-MLP(53)lowast 7299⋆⋆⋆ 8460⋆⋆⋆ 8382⋆⋆⋆ 8342⋆⋆⋆ 8878⋆⋆⋆

Consider both the CNY and CNH from January 3 2011 to December 21 2015 with a total of 1304 observations is table compares the forecastingperformance in terms of Dstat for several forecasting models We report Dstat as percentage for l-day ahead predictions where l 1 5 10 20 and 30Moreover we examine the ability of all models to predict the direction of change by the DAC test [40] ⋆⋆⋆ ⋆⋆ and ⋆ denote statistical significance at 1 5and 10 respectively For each length of prediction we mark the maximum Dstat as bold

12 Complexity

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

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Page 13: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

extremely high transaction costs the erosion of profitsshould not be ignored and it usually makes the tradingstrategy fail in reality erefore letting τ be larger than zerocan reduce the number of trades More importantly τ couldbe regarded as a confidence level indicator which produceslong and short trading thresholds ie ps(1 + τ) andps(1 minus τ) Only when the l-day ahead prediction 1113954ps+l islarger (smaller) than the thresholds we long (short) theCNY Specifically when we set τ 1 denoting that if theforecast price exceeds the present price by more than 1 webuy it on the contrary if the forecast price exceeds thepresent price by less than 1 we short it To fit the practicalsituation this empirical analysis also considers annualreturns with transaction costs of 00 01 02 and 03respectively

Table 10 discusses the performance of the above tradingstrategy with τ 0 05 1 based on best models selectedaccording to Tables 2 and 3 It displays the best performancemodels with different forecasting periods e returnsshown in the last four columns have been adjusted to annualreturns using different transaction costs Firstly it can beseen that the larger the l is which means the forecastingperiod is longer the larger the standard deviation will be Ifthere is no transaction cost the return decreases with theincrease of the forecasting period l For instance in Panel Achoosing a forecasting period of 1 day with τ 0 and zerotransaction cost the annual return will reach 1359 bychoosing the best performance model EMD(-1)-MLP(3)lowastHowever extending the forecasting period to 30 days thereturn will become 459 with the best performance model

However if transaction costs are considered it is clearthat the return increases as the forecasting period becomeslonger which is opposite to the case where there are notransaction costs e annual return suffers significant fallsin short forecasting periods after considering the transaction

cost since the annual return of a short period is offset by thesignificant cost of high-frequency trading For instance witha 03 trading cost the annual return of the best perfor-mance model for 30-day ahead forecasting is positive and isonly 209 but the annual return of EMD(-1)-MLP(3)lowastwhich is the best performance for forecasting 1-day aheadreaches as low as minus 6141 e annual return decreases withincreasing transaction costs for every forecasting period

Panels B and C respectively display trading strategyperformance based on the best model when τ 05 andτ 1 e 1-day forecasting case is ignored in this ex-periment since the predicted value of the 1-day period doesnot exceed τ e standard deviation in the fourth columndecreases with the growth of forecasting periods Anotherfinding in these two panels is that the annual return de-creases as the transaction cost becomes larger in the sameforecasting period which is similar to Panel A Howeverwith the same transaction cost the annual return decreaseswith the growth of the forecasting period which is contraryto the situation in Panel A is may be the result of settingτ 05 or τ 1 the annual return will not be eroded bytrading costs

When we set τ 05 for 5-day ahead forecasting al-though the average annual return with different trading costsis at least 2178 there are only 32 trading activities in a totalof 832 trading days However in choosing long periodforecasting such as 20 days ahead trading activity is 220with a 84 average annual return In Panel C the tradingactivities are less than in Panel B If a 03 trading cost withτ 1 is considered the annual return of 30-day aheadforecasting will exceed 10 and there are more than 130trading activities It can be seen that trading activities reducewith the growth of critical number τ To sum up applyingEMD-MLPlowast to forecast the CNY could produce some usefultrading strategies even considering reasonable trading costs

Table 10 Performance of trading strategy based on the best EMD-MLP

Ns SDReturn with transaction cost ()

00 01 02 03

Panel A τ 01-day EMD(-1)-MLP(3)lowast 812 146 1359 minus 1141 minus 3641 minus 61415-day EMD(-1)-MLP(3)lowast 822 153 712 212 minus 288 minus 78810-day EMD(-1)-MLP(53)lowast 830 170 619 369 119 minus 13120-day EMD(-1)-MLP(53)lowast 823 176 498 373 248 12330-day EMD(-2)-MLP(53)lowast 823 173 459 376 292 209Panel B τ 055-day EMD(-1)-MLP(3)lowast 32 365 3678 3178 2678 217810-day EMD(-1)-MLP(53)lowast 112 280 1918 1668 1418 116820-day EMD(-1)-MLP(53)lowast 220 203 1215 1090 965 84030-day EMD(-2)-MLP(53)lowast 364 175 830 747 664 580Panel C τ 15-day EMD(-1)-MLP(3)lowast 5 493 8502 8002 7502 700210-day EMD(-1)-MLP(53)lowast 17 472 4020 3770 3520 327020-day EMD(-1)-MLP(53)lowast 71 229 1842 1717 1592 146730-day EMD(-2)-MLP(53)lowast 131 172 1308 1224 1141 1058In terms of NMSE and Dstat we select the best models to forecasting l-day ahead predictions where l 1 5 10 20 and 30e third column shows the samplesize in each model and is denoted as Ns By the trading strategy rule as (11) with τ 0 we generate Ns l-day returns e fourth column reports the standarddeviation of the annualized returns without transaction cost e last four columns represent the averages of Ns annualized returns with different transactioncosts

Complexity 13

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 14: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

4 Conclusions

In this paper RMB exchange rate forecasting is investigatedand trading strategies are developed based on the modelsconstructed ere are three main contributions in thisstudy First since the RMBrsquos influence has been growing inrecent years we focus on the RMB including the onshoreRMB exchange rate (CNY) and offshore RMB exchange rate(CNH) We use daily data to forecast RMB exchange rateswith different horizons based on three types of models ieMLP EMD-MLP and EMD-MLPlowast Our empirical studyverifies the feasibility of these models Secondly in order todevelop reliable forecasting models we consider not only theMLP model but also the hybrid EMD-MLP and EMD-MLPlowastmodels to improve forecasting performance Among all theselected models the EMD-MLPlowast performs best in terms ofboth NMSE and Dstat criteria It should be noted that theEMD-MLPlowast is different from the methodology proposed byYu et al [27] We regard some IMF components as noisefactors and delete them to reduce the volatility of the RMBe empirical experiments verify that the above processcould clearly improve forecasting performance For exam-ple Table 1 shows that the best models are EMD(-1)-MLP(3)lowast EMD(-1)-MLP(53)lowast and EMD(-2)-MLP(53)lowastFinally we choose the best forecasting models to constructthe trading strategies by introducing different criticalnumbers and considering different transaction costs As aresult we abandon the trading strategy of τ 0 since theannual returns are mostly negative However given τ 05or 1 all annual returns are more than 5 even includingthe transaction cost In particular by setting τ 1 with03 transaction cost the annual return is more than 10 indifferent forecasting horizonsus this trading strategy canhelp investors make decisions about the timing of RMBtrading

As the Chinese government continues to promotingRMB internationalization RMB currency trading becomesincreasingly important in personal investment corporatefinancial decision-making governmentrsquos economic policiesand international trade and commerce is study is tryingto apply the neural network into financial forecasting andtrading area Based on the empirical analysis the forecastingaccuracy and trading performance of RMB exchange ratecan be enhanced Considering the performance of thisproposed method the study should be attractive not only topolicymakers and investment institutions but also to indi-vidual investors who are interested in RMB currency orRMB-related products

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

All authors have contributed equally to this article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (NSFC no 71961007 71801117 and71561012) It was also supported in part by Humanities andSocial Sciences Project in Jiangxi Province of China (JJ18207and JD18094) and Science and Technology Project of Ed-ucation Department in Jiangxi Province of China(GJJ180278 GJJ170327 and GJJ180245)

References

[1] M Fratzscher and A Mehl ldquoChinarsquos dominance hypothesisand the emergence of a tri-polar global currency systemrdquoeEconomic Journal vol 124 no 581 pp 1343ndash1370 2014

[2] C R Henning ldquoChoice and coercion in East Asian exchange-rate regimesrdquo Power in a Changing World Economy Rout-ledge pp 103ndash124 2013

[3] C Shu D He and X Cheng ldquoOne currency two markets therenminbirsquos growing influence in Asia-Pacificrdquo China Eco-nomic Review vol 33 pp 163ndash178 2015

[4] A Subramanian and M Kessler ldquoe renminbi bloc is hereAsia down rest of the world to gordquo Journal of Globalizationand Development vol 4 no 1 pp 49ndash94 2013

[5] R Craig C Hua P Ng and R Yuen ldquoChinese capital accountliberalization and the internationalization of the renminbirdquoIMF Working Paper 2013

[6] M Funke C Shu X Cheng and S Eraslan ldquoAssessing theCNH-CNY pricing differential role of fundamentals con-tagion and policyrdquo Journal of International Money and Fi-nance vol 59 pp 245ndash262 2015

[7] M Khashei M Bijari and G A Raissi Ardali ldquoImprovementof auto-regressive integrated moving average models usingfuzzy logic and artificial neural networks (ANNs)rdquo Neuro-computing vol 72 no 4ndash6 pp 956ndash967 2009

[8] Z-X Wang and Y-N Chen ldquoNonlinear mechanism of RMBreal effective exchange rate fluctuations since exchange re-form empirical research based on smooth transition auto-regression modelrdquo Financial eory amp Practice vol 6 p 42016

[9] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networks the state of the artrdquo InternationalJournal of Forecasting vol 14 no 1 pp 35ndash62 1998

[10] G P Zhang ldquoAn investigation of neural networks for lineartime-series forecastingrdquo Computers amp Operations Researchvol 28 no 12 pp 1183ndash1202 2001

[11] C H Aladag and M M Marinescu ldquoTlEuro and LeuEuroexchange rates forecasting with artificial neural networksrdquoJournal of Social and Economic Statistics vol 2 no 2 pp 1ndash62013

[12] L Yu G Hang L Tang Y Zhao and K Lai ldquoForecastingpatient visits to hospitals using a WDampANN-based de-composition and ensemble modelrdquo Eurasia Journal ofMathematics Science and Technology Education vol 13no 12 pp 7615ndash7627 2017a

[13] Y Kajitani K W Hipel and A I McLeod ldquoForecastingnonlinear time series with feed-forward neural networks acase study of Canadian lynx datardquo Journal of Forecastingvol 24 no 2 pp 105ndash117 2005

14 Complexity

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 15: Chinese Currency Exchange Rates Forecasting with EMD-Based ...downloads.hindawi.com/journals/complexity/2019/7458961.pdf · Research Article Chinese Currency Exchange Rates Forecasting

[14] L Yu Y Zhao and L Tang ldquoEnsemble forecasting forcomplex time series using sparse representation and neuralnetworksrdquo Journal of Forecasting vol 36 no 2 pp 122ndash1382017

[15] L Cao ldquoSupport vector machines experts for time seriesforecastingrdquo Neurocomputing vol 51 pp 321ndash339 2003

[16] L Yu H Xu and L Tang ldquoLSSVR ensemble learning withuncertain parameters for crude oil price forecastingrdquo AppliedSoft Computing vol 56 pp 692ndash701 2017b

[17] L Yu Z Yang and L Tang ldquoQuantile estimators with or-thogonal pinball loss functionrdquo Journal of Forecasting vol 37no 3 pp 401ndash417 2018

[18] M Alvarez-Diaz and A Alvarez ldquoForecasting exchange ratesusing genetic algorithmsrdquo Applied Economics Letters vol 10no 6 pp 319ndash322 2003

[19] C Neely P Weller and R Dittmar ldquoIs technical analysis inthe foreign exchange market profitable A genetic pro-gramming approachrdquo e Journal of Financial and Quanti-tative Analysis vol 32 no 4 pp 405ndash426 1997

[20] L Yu S Wang and K K Lai Foreign-xchange-ate Forecastingwith Artificial Neural Networks vol 107 Springer Science ampBusiness Media Berlin Germany 2010

[21] G P Zhang ldquoTime series forecasting using a hybrid ARIMAand neural network modelrdquo Neurocomputing vol 50pp 159ndash175 2003

[22] M Alvarez-Dıaz and A Alvarez ldquoGenetic multi-modelcomposite forecast for non-linear prediction of exchangeratesrdquo Empirical Economics vol 30 no 3 pp 643ndash663 2005

[23] L Zhao and Y Yang ldquoPSO-based single multiplicative neuronmodel for time series predictionrdquo Expert Systems with Ap-plications vol 36 no 2 pp 2805ndash2812 2009

[24] W K Wong M Xia and W C Chu ldquoAdaptive neuralnetwork model for time-series forecastingrdquo European Journalof Operational Research vol 207 no 2 pp 807ndash816 2010

[25] L Yu Y Zhao L Tang and Z Yang ldquoOnline big data-drivenoil consumption forecasting with google trendsrdquo In-ternational Journal of Forecasting vol 35 no 1 pp 213ndash2232019

[26] N E Huang Z Shen S R Long et al ldquoe empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical and En-gineering Sciences vol 454 no 1971 pp 903ndash995 1998

[27] L Yu SWang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[28] C-F Chen M-C Lai and C-C Yeh ldquoForecasting tourismdemand based on empirical mode decomposition and neuralnetworkrdquo Knowledge-Based Systems vol 26 pp 281ndash2872012

[29] C-S Lin S-H Chiu and T-Y Lin ldquoEmpirical modedecompositionndashbased least squares support vector regressionfor foreign exchange rate forecastingrdquo Economic Modellingvol 29 no 6 pp 2583ndash2590 2012

[30] L Tang Y Wu and L Yu ldquoA non-iterative decomposition-ensemble learning paradigm using RVFL network for crudeoil price forecastingrdquo Applied Soft Computing vol 70pp 1097ndash1108 2018

[31] M Alvarez Dıaz ldquoSpeculative strategies in the foreign ex-change market based on genetic programming predictionsrdquoApplied Financial Economics vol 20 no 6 pp 465ndash476 2010

[32] W Huang K Lai Y Nakamori and S Wang ldquoAn empiricalanalysis of sampling interval for exchange rate forecasting

with neural networksrdquo Journal of Systems Science andComplexity vol 16 no 2 pp 165ndash176 2003b

[33] A Nikolsko-Rzhevskyy and R Prodan ldquoMarkov switchingand exchange rate predictabilityrdquo International Journal ofForecasting vol 28 no 2 pp 353ndash365 2012

[34] M Riedmiller and H Braun ldquoA direct adaptive method forfaster backpropagation learning the RPROP algorithmrdquo inProceedings of the IEEE International Conference on NeuralNetworks pp 586ndash591 IEEE San Francisco CA USAMarch-April 1993

[35] N E Huang and Z Wu ldquoA review on Hilbert-Huangtransform method and its applications to geophysical stud-iesrdquo Reviews of Geophysics vol 46 no 2 2008

[36] N E Huang M-L C Wu S R Long et al ldquoA confidencelimit for the empirical mode decomposition and Hilbertspectral analysisrdquo Proceedings of the Royal Society of LondonSeries A Mathematical Physical and Engineering Sciencesvol 459 no 2037 pp 2317ndash2345 2003a

[37] J Yao and C L Tan ldquoA case study on using neural networksto perform technical forecasting of forexrdquo Neurocomputingvol 34 no 1ndash4 pp 79ndash98 2000

[38] F X Diebold and R S Mariano ldquoComparing predictiveaccuracyrdquo Journal of Business amp Economic Statistics vol 20no 1 pp 134ndash144 2002

[39] L Yu S Wang and K K Lai ldquoA novel nonlinear ensembleforecasting model incorporating GLAR and ANN for foreignexchange ratesrdquo Computers amp Operations Research vol 32no 10 pp 2523ndash2541 2005

[40] M H Pesaran and A Timmermann ldquoA simple non-parametric test of predictive performancerdquo Journal of Busi-ness amp Economic Statistics vol 10 no 4 pp 461ndash465 1992

[41] S Anatolyev and A Gerko ldquoA trading approach to testing forpredictabilityrdquo Journal of Business amp Economic Statisticsvol 23 no 4 pp 455ndash461 2005

Complexity 15

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

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