Time Series Forecasting International Tourism Arrival to Thailand 2006-2010 E-research IMF

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Time Series Forecasting : International Tourist

Arrivals to Thailand (Working paper No. 6/2006)

N. Rangaswamy Ph.D.

Professor & Chairman , Department of Economics, Bangalore University, Bangalore

Chukiat Chaiboonsri Received a scholarship from the Indian Government study Ph.D. (Economics)

at Bangalore University from 2005-2010. [email protected]

Economics Department Bangalore University

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Preface

I would like to thanks Dr. N. Rangaswamy, Professor & Chairman of the Department of Economics at Bangalore University. He is both my professor and adviser at Bangalore University for the period from 2005 to 2010. And I would like to thanks ICCR scholarship (India government organization) that gave funds to me for study a Ph.D.(Economics) at Bangalore University during the same period. This working paper is a part of the study for my Ph.D. Furthermore my grateful thanks to Assoc,Prof. Dr. Prasert Chaitip, my father, my mother, my wife and my relative for their help and support in every way. This working paper was edited by Macus Vigilante, lecturer at Payap University, Chiang Mai . So I would like to thanks you and I hope that you can help me on my next paper. Finally my special thanks to God because He blesses me in every day when I walk with Him.

Mr. Chukiat Chaiboonsri

Department of Economics Bangalore University

Bangalore, India

16/12/2006



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Contents

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Preface A Contents B Tables C Figure D Abstract 1 1. Introduction 2 2. Research Aim and Objective 3 3. Study area in this research 3 4. The research Framework of tourism forecasting and forecasting methodology

4.1 The method for forecasting a single variable 4 4.1.1 Holt-winter 4 4.1.2 ARIMA Modelling 5

4.1.3 Neural Network Method 9 4.2 The method of forecasting from more variables 11 4.2.1 VAR Model 11 4.2.2 GMM method for time series analysis 12 4.2.3 ARCH-GARCH Model 13 4.2.4 ARCH-M Model and GARCH-M Model 14 4.2.5 TARCH Model 15 4.2.6 EGARCH Model 15 4.2.7 PARCH Model 16

5. The results of the research 5.1 Forecasting accuracy is based on the Mean Absolutes Percent 17

Error(MAPE) of each method (the method of forecasting from a single variable)

5.2 Forecasting accuracy is based on Mean Absolutes Percent 18 Error(MAPE) for each method(More variable)

5.3 The empirical results of forecasting international tourism demand 19 arrivals to Thailand for 2006-2010.

6. The conclusions of research and policy recommendations 20 Bibliography 21 Appendix A. 24 Appendix B. 25

C



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Tables

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1. Table 1 : Accuracy comparison in sample for different forecasting 18

models based on the single variable method.

2. Table 2 : Accuracy comparison in sample for different forecasting 18 models based on the multi variable methods for forecasting.

3. Table 3 : Forecasts of quaternary percentage change in 19 international tourist arrivals to Thailand based on the SARIMA(0,1,1)(0,1,4) model during the period 2006-2010

4. Table 4 : Forecasts of quaternary percentage change in 19 international tourist arrivals to Thailand based on the VAR model for the period 2006-2010.

5. Table 5 : Forecasts the number of international tourist 24

arrivals to Thailand for 2006(Q1)-2010(Q4) based on the SARIMA forecasting method.

6. Table 6 : Forecasts the number of international tourist 25 arrivals to Thailand for 2006(Q1)-2010(Q4) based on the VAR Method.



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D

Figure

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1. Figure 1 : Graphical presentation of forecasting international 24

tourist arrivals to Thailand for 2006-2010 based on the SARIMA forecasting method.

2. Figure 2 : Graphical presentation of forecasting international 25 tourist arrivals to Thailand for 2006-2010 based on the VAR forecasting method.



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Time series forecasting : international tourist arrivals to Thailand*

Chukiat Chaiboonsri, Candidate in the Indian Government Ph.D. (Economics) program

at Bangalore University, 2005-2010. [email protected]

Parsert Chaitip Ph.D.

Assoc, Prof. DR. in Faculty of Economics, Chiang Mai University, Chiang Mai .

N. Rangaswamy Ph.D. Professor & Chairman , Department of Economics, Bangalore University, Bangalore

Abstract

Forecasting is an essential analytical tool in tourism policy and planning. This paper focuses on forecasting methods based on two concepts to forecast international tourism arrivals to Thailand for 2006-2010. The first forecasting method establishes a single variable and the second forecasting method establishes more variables. The following forecasting methods were employed in this paper: SARIMA, ARIMA, Holt-Winter-Additive, Holt-Winter-Multiplicative, Holt-Winter-No seasonal, Neural network, VAR, GMM estimation for time series analysis, ARCH-GARCH-M, ARCH-GARCH, TARCH, PARCH and EGARCH. Secondary data were used to produce forecasts of international tourist arrivals to Thailand for 2006-2010 based on the period 1997-2005. The results confirm that the best forecasting method based on the first concept is SARIMA(0,1,1)(0,1,4) and the best forecasting method based on second concept is the VAR model. Furthermore both the SARIMA model and VAR model predict that international tourism arrivals to Thailand for 2006-2010 will growth at a positive rate. If these results can be generalized for future year, then it suggests that both the Thai government sector and private tourism industry sector should prepare to receive increasing numbers of international tourist arrivals to Thailand in this period. Keywords: international tourism of Thailand; best forecasting methods; single variable; multi variable ------------------------- * This paper has been accepted for presentation in international conference namely The 2nd SSEASR Conference of SOUTH AND SOUTHEAST ASIAN ASSOCIATION FOR THE STUDY OF CULTURE AND RELIGION May 24-27, 2007, Thailand


mailto:[email protected]


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1. Introduction International tourist arrivals and international tourist receipts have traditionally been used as benchmark aggregate series to assess the overall importance of tourism worldwide and in specific countries. High international tourist arrival levels may be used in advertising campaigns and also in political discussions to legitimize and emphasize the success of a country in the international community. Similarly, sizeable international tourist receipts can be a good indicator of the role of tourism in an economy in term of both Gross Domestic Product and foreign exchange generation. Policy makers may subsequently be convinced to assist tourism development and further increase profitability from tourism activities. It is not surprising, therefore, that the majority of World Tourism Organization (WTO) statistics focus on these two time series reported as levels, annual changes and market shares (Papatheodorou and Song 2005). Furthermore The United Nations Conference on Trade and Development singled out tourism as the only sector in international trade in services for which developing countries had experienced positive surpluses in their trade account (UNCTAD, 1998). Tourism receipts in developing countries, valued at US$ 6 billion in 1980, reached an unprecedented US$ 62.2 billion in 1996. The prognosis is that this surge will continue, a manifestation of the growing importance of tourism (Narayan, 2005). The above information emphasizes that international tourism can generate money for the economy of developing countries, such as Thailand. In 2003, Thailand 10,082,109 million international tourists and in the same year Thailand received income from international tourism of 309,269 million baht. And in 2004, the number of international tourists was 11,737,413 million and the income was 384,359 million baht. This data shows that when the number of international tourists to Thailand increases, then the income from international tourists to Thailand also increases. Therefore, if the econometrics approach is able to forecast the number of international tourist arrivals to Thailand, it will also be able to forecast the level of income from international tourists. Thus it is an essential analytical tool in tourism policy and planning. This paper focus on the econometrics approach for forecasting the number of international tourist arrival to Thailand for the period 2006-2010 based on data from the period 1997-2005. The various forecasting models developed in reference to tourism can be broadly classified into four categories (Kamra, 2006): (a) Structural Models; (b) Trend Extrapolation Models; (c) Simulation Model; and Qualitative Modes. Structural Models are based on establishing the relationship between some measure of tourism demand and a series of causal variables, such as price, income, motivation, image, competition, or distance. Trend Extrapolation Models, also known as Time-Series models, by their very name, depend on the extrapolation of a historical series of data into the future. The two variables are some measure of tourism demand/market activity and time. Simulation Models, a complex set of equations, are a distinctive combination of both Structural Models and Trend Extrapolation Models resulting in a more comprehensive systems simulation. And lastly, Qualitative Models are primarily non-mathematical models. The most widely acknowledged and most commonly used qualitative forecasting model is the Delphi Model. Once again, this paper will forecast international tourist arrival to Thailand for 2006-2010 based on two categories: (a) Structural Models, in this paper



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called multi variable forecasting methods, (b) Trend Extrapolation Models, in this paper called single variable forecasting methods. 2. Research Aim and Objective This research aims to seek the best forecasting method for forecasting international tourist arrivals to Thailand for the period 2006-2010 and to predict the number of international tourist arrivals to Thailand in this period. 3. Scope of this research The scope of this research is the period 1997-2010 and mostly the data was secondary data. The countries used for forecasting international tourist arrivals to Thailand were all the countries of importance to the international tourism industry of Thailand (source: Thailand’s Tourism Organization). The variables used in this research were the number of international tourist arrivals to Thailand from 1997-2005 to forecast for 2006-2010 and the income growth rate of the country’s industry based on period 1997-2005 to forecast for 2006-2010. 4. The research framework of tourism forecasting and forecasting methodology Tourism forecasting methods can be divided into qualitative and quantitative methods and causal quantitative techniques. Regardless of the type of forecasting method used, the usefulness of any tourism demand forecasting model is really determined by the accuracy of the tourism forecasts that it can generate, as measured by comparison with actual tourism flows (Mahmoud, 1984). Frechtling (1996, 2001) highlighted five patterns in a tourism time series: (a) seasonality, (b) stationarity, (c) linear trend, (d) non-linear trend and (e) stepped series. The time series non-causal approach or forecasting a single variable approach is limited by the lack of explanatory variables and it also was best used for short-term to medium-term forecasting. Additionally, in this approach, it is assumed that the factors related to seasonality, trend and cycle are slow to change and can be extrapolated in the short term (Kon and Turner, (2005)). In this paper, two types of time series forecasting methods were used, namely single variable methods and multi variables methods (Hall, Lilien, Sueyoshi, Engle, Johnston and Ellsworth (2005)). Examples of single variable forecasting methods are: the Holt-winter method, the ARIMA method, the SARIMA method and the Neural Network method. Examples of the second method of forecasting, multi variable, are: the VAR model, the GMM method, the ARCH-GARCH method, the ARCH-GARCH-M method, the TARCH method, the EGARCH method and the PARCH method.



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4.1 The method for forecasting from a single variable

4.1.1 Holt-winter

Holt-Winter-No seasonal (Two parameter) Holt’s method is the basic trend model, Ŷt+1 = estimated level t + trend t , combined with exponential smoothing as well as where (a) is estimated level t and (b) is trend t. these two coefficients are defined by the following recursion: (see equation 1E and equation 2E).

a(t) = α y t +(1- α )( α (t-1) + b ( t-1)) --------- ( 1E ) b(t) = β( a(t) – a(t-1)) + 1 – β b(1- t ) --------- ( 2E )

Where 0 < α, β < 1 and γ = 0 are damping factors as well as this is an exponential smoothing method with two parameters and forecasts are computed by : (see equation 3E ).

Ŷ T +k = a(T) + b(T)k --------- ( 3E )

where

Ŷ T + k = time series variable has been to forecast at time T +k or the smoothed series Ŷ t + k a(T) = a(t) b(T) = b(t)

Holt-Winter-Additive (Three parameter) This method is appropriate for series with a linear time trend and additive seasonal variation and the smoothed series Ŷ t + k is give by: (see equation 4E).

Ŷ t +k = a + b k +c t + k --------- 4E where

a = estimated level t or intercept term b = trend t c = seasonal t + k Ŷ t +k = time series variable that has been forecasted at time t+k or the smoothed series Ŷ t +k

also where a(t) = α (y t – c t( t – s )) + (1- α)( a (t-1) + b( t -1) )

b(t) = β( a(t) – a(t-1)) + 1 – β b( t - 1) c(t) = γ( y t – a(t +1)) + γct( t - s)

Where 0 < α, β < 1 and γ < 1 are damping factors and s is the seasonal frequency specified in the cycle for seasonal and forecasts are computed by : ( see equation 5E ).



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Ŷ T +k = a(T) + b(T) k +c T + k -s --------- 5E where

a(T) = a(t) b(T)k = b(t) c T+ k - s = c t( t)

Holt-Winter-Multiplicative (Three parameter) The Holt-winters Multiplicative method is the basic multiplicative seasonal trend model. This method is appropriate for series with a linear time trend and multiplicative seasonal variation. The smoothed series ŷ t is give by: (see equation 6E).

ŷ t +k = ( a + b k ) c t + k --------- 6E

where

a = permanent component ( intercept term ) or estimated level t b = trend t c t = multiplicative seasonal factor

The above three coefficients from equation 6E are defined by the following recursion:

a(t) = α [y t / c t( t – s )] + (1- α)( a (t-1) + b( t -1) ) b(t) = β( a(t) – a(t-1)) + (1 – β) b( t - 1) c(t) = γ( y t / a(t)) + (1-γ)ct( t - s)

Where 0 < α, β < 1 and γ < 1 are damping factors and s is the seasonal frequency specified in the cycle for seasonal and forecasts are computed by : ( see equation 7E ).

Ŷ t +k = ( a(T) + b(T) k ) c T + k - s --------- 7E

As well as where the seasonal factors are used from the last s estimates and where a(T) = a(t), b(T) = b(t) and c t + k - s = c t (t).

4.1.2 ARIMA modelling

The ARIMA modelling autoregressive term integrated moving-average term and autoregressive term can be written by : (see equation 8E ).



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y t +k = µ + γ y t – 1 + ε t --------- 8E Equation 8E is said to be first order autoregressive ( or-self-regressive ) because under certain assumptions E[ y t | y t – 1] = γ y t – 1. A more general p th-order autoregressive term or AR(p) process would be written give by : (see equation 9E). y t = µ + γ1 y t – 1 + γ2 y t – 2 +……+ γp y t – p + ε t --------- 9E where y t = time series data µ = constant term γ1 = coefficient of AR(p) And first order moving-average term or MA(1) specification also can be written give by equation 10E. y t = µ + ε t - θ ε t-1 --------- 10E or y t = µ + (1- θ L)ε t --------- 10E As well as more general q th-order moving-average term or MA(q) process would be written give by : (see equation 11E). y t = µ + ε t - θ1 ε t-1 - θ2 ε t-2 -…….- θq ε t-q --------- 11E An autoregressive and moving-average (ARMA(1,1)) process can be written give by equation 12E. y t = µ + γ1 y t – 1 + ε t - θ1 ε t-1 --------- 12E The equation 12E as first order autoregressive term (AR(1)) and first order moving-average term (MA(1)) as well as ARMA(p,q) process can be written give by: (see equation 13E). y t = µ + γ1 y t – 1 + γ2 y t – 2 +……+ γp y t – p + ε t - θ1 ε t-1 - θ2 ε t-2 -…….- θq ε t-q -------- 13E where

y t = time series data at t time µ = constant term γ1 = coefficient of AR(1) ε t = error term at t time θ 1 = coefficient of MA (1)

An autoregressive integrated moving-average (ARIMA) process is ARIMA(p,d,q) modelling and can be written give by: (see equation 14E and 15E).



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Ø(β )∆dy t = δ + θ(β) ε t --------- 14E with Ø(β ) = 1- Ø1 β - Ø 2 β2 -……- Ø p βp

and Ø(β ) = 1- θ 1(β) - θ 2(β)2 - …….- θ q(β)q where Ø(β ) = The autoregressive operator at order p ∆dy t = differencing operator at order d of time series data y t δ = constant term θ(β) = moving-average operator at order q ε t = error term of equation 14E Furthermore, full ARIMA(p,d,q) model for time series forecasting also can be written give by equation 15E. y t = µ + γ1∆dy t -1 + γ2 ∆d y t-2 +……+ γ p ∆d

y t – p + ε t - θ1 ε t-1 - θ2 ε t-2 -…….- θ q ε t-q -------- 15E The BOX-JENKINS(BJ) method which has become the standard for estimating ARIMA(p,d,q) model was developed by G.E.P Box and G.M Jenkins (Time series analysis, Forecasting, and control, San Francisco, Holden Day, 1970). The procedure involves making successive approximation though four stages: Identification, Estimation, Diagnostic Checking and Forecasting (see figure 1 for more detail).



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Yes No

From :Gujarati(2003)

Figure 1 : Stage of Box-Jenkins (BJ) method for estimates ARIMA(p,d,q) modelling process.

Seasonal ARIMA or SARIMA is an extension of ARIMA where seasonality is accommodated by seasonal differencing. SARIMA(p.d.q)(P,D,Q) is applied to data with an annual seasonal pattern P,D and Q in the seasonal part of the model represent the order autoregression, differencing and moving-average respectively and as quarterly data are used, for period s = 4 is defined as: ∆ s y t = y t - y t - s or ∆ 4 y t = y t - y t - 4

Identification of the model ( choosing tentative p,q,d)

Estimation (parameter estimation of

the chosen model)

Diagnostic checking (Are the estimated

residuals white noise?)

Forecasting



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4.1.3 Neural network method Neural network models or ANN models consists of an input layer, and output layer, and usually one or more hidden layer. Each of these layers contains nodes, and these nodes are connected to nodes at adjacent layer(s). Figure 2 demonstrates a simplified neural network with three layers.

w1 w2 w3 w13 w11 w12 w21 w22 w23

From: Rob Law and Norman Au (1999)

Figure 2 : A neural network model with three layers

And figure 2 shows a system of the neural network model and the mathematically of this model also can be written give by : (see equation 16E)

y j = Σ2i =1

x i w i j --------- 16E

where y1 = x 1 w 11 + x 2 w 21 y2 = x1

w 12 + x 2 w 22 y3 = x1

w 13 + x 2 w 23

and also where y j = the variable in hidden layer x i = the variables in input layer w i j = weighted of x i

Y

y1 y2

y3

x2

x1 Input layer

Hidden layer

Output layer



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And a sigmoid function (YT ) in the following from is used to transform the output so that it falls into an acceptable range. This transformation is done before the output reaches the next level. The purpose of a sigmoid function is to prevent the output value from begin too large, as the value of (YT ) must fall between 0 and 1: see equation 17E). y T = 1/ ( 1+ e-y

) --------- 17E Finally, Y, a node of the output layer in figure 2 is obtained by the following summation function : (see equation 18E ).

Y = Σ3i =1

Y T i w i --------- 18E

where

Y = ( Y T 1 w 1 ) + ( Y T 2 w 2 ) + ( Y T 3 w 3 ) w i = weighted of Y T i Y = also the variable in output layer

Equation 1E to equation 18E can be written in linear equation function form: (see equation 19E).

Y = ƒ( x 1 ,x2 ) --------- 19E where

Y = dependent variables ( output layer) x 1 x 2 = weighted of Y T i ƒ = neural network function

A neural network model was used for forecasting tourism demand such as Uysal and Roubi (1999) to compare the use of the ANN against multiple regression in tourism demand analysis, Law and AU (1999) used a supervised feed-forward neural network causal model to forecast annual Japanese tourist arrivals in Hong Kong, Tsaur et al (2002) used ANNs to analyze guest loyalty to international tourist hotels and find that ANNs demonstrate satisfactory model-fitting performance and Sen and W.Turher (2005) used ANNs to forecast internal tourism demand arrivals to Singapore. The above research shows that the neural network method has become popular for forecasting tourism demand models.



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4.2 The method of forecasting from more variables 4.2.1 VAR model The vector autoregressive models or VAR models were developed by C.A. Sim in 1980. These models having the term autoregressive is due to the appearance of the lagged value of the dependent variable on the right-hand side and the term vector is due to the fact that of a vector of two (or more) variables. The basic model considered in following is a vector autoregressive (VAR) model possibly including deterministic terms and with independent Gaussian error: the k-dimensional time vector yt is generated by a vector autoregressive process of order p, denoted VAR(p) model(see equation 1F). yt = А1 yt-1 +……+ Аp yt-p + βdt + εt ------------- 1F where t = 1,….., T А i β = coefficient matrices y0 = ( y0 , …., y1-p) yt = time series data And the innovation process εt is an unobservable zero-mean white noise process with a time-invariant positive-definite variance-covariance matrix Σ, εt = yt - E [yt | yt-1] and which is assumed to be Gaussian : εt ~ NID (0, Σ). Thus the expectation of yt conditional on the information set yt-1= ( yt-1, yt-2,……., y1-p) as give by : (see equation 2F). E [yt | yt-1] = βdt + Σp j=1 А j yt-j ------------- 2F Where t = 1,….., T βdt = intercept term yt ,yt-1 = time series data

А j = coefficient of VAR model The information criteria considered the best of VAR model to forecasting are defined as follow : AIC = -2 (L/T) + (K/T) SC = -2(L/T) + k log(T)/T HQ = -2(L/T) + 2k (log(T)/T and



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Modified AIC(MAIC) = -2 (L/T) + 2((K+e)/T) Modified SC(MSC) = -2 (L/T) + (K+e) log(T)/T Modified HQ(MHQ) = -2 (L/T) + 2(K+e)log(T)/T where e = α2 εt y2 t-1

y t-1 = yt as defined in autoregressive spectral

L = - TM/2 (1+log2Π) –T/2log|Ω| |Ω| = det ( Σi ε ε /T) M = the number of equation T = Number of observation 4.2.2 GMM method for time series analysis The general method of moment (GMM) as the GMM estimator belongs to a class of estimators know as M-estimators that are defined by minimizing some criterion function. This estimator has been developed by Hansen and Singleton (1992) and the benefits of this method are multiple, for example: the GMM can be made robust to heteroscedasticity and or autocorrelation of unknown form, GMM is a robust estimator in that it does not require information of exact distribution of the disturbance and GMM is an estimator that ensures consistent parameter estimates under a wide variety of conditions and that does not require the assumption of normality. The GMM**/ estimator for time series data starts by considering the linear regression model (see equation 1G). y = xβ + µ ------------- 1G and E [ µµ΄ ] = Iσ2 E [ xµ΄ ] = 0 { this is known as an orthogonal condition} V [ x΄µ ] = (x΄x)σ2

where E [ µµ΄ ] = expected error term of equation 1G E [ xµ΄ ] = expected mean of equation 1G

V [ x΄µ ] = variance of equation 1G

The OLS estimator are obtain by minimizing µ΄µ or (y - xβ)΄( y - xβ ) as well as the generalized method of moment (GMM) estimation method minimizes µ΄x w x΄µ or (y - xβ)΄x w x΄( y - xβ ) and see equation 2G. β^ = (x΄x)-1 x΄ y ------------- 2G (x΄x) β^ = x΄ y ------------- 2G ---------------------- **/ It has been explained by G.S Maddala(2002). Introduction To Econometrics third edition Published by John Wiley & Son Ltd India.



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And give x w x΄ in to equation 2G both right hand side and left hand side as well as can be written give by : (see equation 3G) ( x w x΄)(x΄x) β^ = x΄ y (x w x΄ ) ------------- 3G ( x x΄w x΄x) β^ = x΄ x w x΄y ------------- 3G where (x΄x) = nonsingular matrix w = weighting matrix and it is nonsingular matrix Let z be the set of instruments variable and z is of the same dimension as x as well as write the orthogonally condition as E(z΄µ ) = 0 and V(z΄µ ) = (z΄z) σ2. The GMM minimizes µ΄z w z΄ µ or (y - xβ)΄zw z΄( y - xβ ) and take z w z΄ in to equation 4G both right hand side and left hand side also can be written give by: (see equation 4G). ( z w z΄)(x΄x) β^ = x΄ y (z w z΄ ) -------------------------- 4G ( x΄z) w (z΄x) β^ = (x΄ z) w z΄ y ------------------------- 4G β^

GMM = [( x΄z) w (z΄x) ]-1(x΄ z w z΄ y) ---------- 4G Hansen (Econometrica,1982) shows that the optimal choice of w is (z΄z)-1/σ2 = [V(z΄µ )]-1 and it is (z΄ Ω z )-1 if E [ µµ΄ ] = Ω , so the GMM in this case as equation 5G. β^

GMM = [ x΄z (z΄Ω z)-1 z΄x]-1[x΄z (z΄ Ω z)-1 z΄y) ---- 5G The covariance matrix of β^

GMM is [ x΄z (z΄Ω z)-1 z΄x]-1 and the GMM method has been used often in the estimation of nonlinear rational expectations model and cases where Ω= E [ µµ΄ ] has a very general specification. 4.2.3 ARCH-GARCH model Engle*** (1982) developed the autoregressive conditional heteroscedasticity (ARCH) model. The key idea of ARCH model is that the variance of µ at time t (=σt 2) depends on the size of the squared error term at time ( t –1),that is, on µ2 t -1 . To be more specific, let revert to the k-variable regression model: (see equation 1H)

Yt = β1 X t + β2 X 2 t +…….+ βk X k t + µ t -------------- ( 1H )

----------------------------- ***/ R.Engle, “ Autoregressive Conditional Heteroscedasticity with Estimates of the variance of UK. Inflation, ” Econometrica, vol. 50 987-1008,1982.



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and assume that conditional on the information available at time (t -1), the disturbance term is distributed as ( see 2H )

µ t ~ N[0,( α 0 + α 1 µ2 t –1) ------------- ( 2H )

that is , µ t is normally distributed with mean zero and variance of ( α 0 + α 1 µ2 t –1). Since in (2H) the variance of µ t depends on the squared disturbance term in the previous time period, it is called an ARCH(1) process. But can generalize it easily. Thus, an ARCH(p) process can be written as: (see equation 3H )

var( µ t ) = σt 2 = α 0 + α 1 µ2 t –1 + α 2 µ2 t –2 +……+ α p µ2 t –p --------- ( 3H )

if there is no autocorrelation in the error variance, and have H0 : α 1 = α 2 =……….=α p = 0 , in which case var(µ t) = α 0 , and have the case of homoscedastic error variance. The generalized autoregressive condition heteroscedasticity (GARCH) model, originally proposed by Bollerslev+/ (1986) which can also be estimated by maximum likelihood. The simplest GARCH model is the GARCH(1,1) model : (see equation number 4H)

σt 2 = α 0 + α 1 µ2 t –1 + λ1σ2 t –1 --------- ( 4H )

Now the variance of the error term has three components: a constant, last period’s volatility (the ARCH term), and last period’s variance (the GARCH term). In general could have any number of ARCH terms and any number of GARCH term and The GARCH (p,q) model refer to the following equation for σt 2 :( see equation 5G )

σt 2 = α 0 + α 1 µ2 t –1 +………+ α p µ2 t –p + λ1σ2 t –1 +…..+λ qσ2 t – q --------- ( 5H )

4.2.4 ARCH-M model and GARCH-M model The ARCH-M model was developed by Engle, Lilien and Robin(1987) and this model can be written give by: (see equation 6H ). yt = x΄t γ + σ2 t γ + εt ------------- 6H A variant of the ARCH-M specification uses condition standard deviation in place of the condition variance. And GARCH-M(1,1) also can be written give by: (see equation 7H and 8H) GARCH-M(1,1) model : yt = x΄t γ + S2 t γ + εt ------------- 7H

σt 2 = w + α i ε 2t + β j σ2 t ---------- 8H ---------------- +/ T. Bollerslev "Generalized Autoregressive Condition Heteroscedasticity" Journal of Econometric vol, 1986, pp 307-236. where



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yt = dependent variable time sires data x΄t = independent variable time sires data γ = coefficient of x΄t S2 t = standard deviation of GARCH-M model γ = coefficient of GARCH-M model

εt = error term of equation 7H σt 2 = variance equation of GARCH-M β j = coefficient of σ2 t α i = coefficient of ε 2t

4.2.5 TARCH model The TARCH model or Threshold ARCH was introduced independently by Zakoian (1990) and Glosten, Jaganathan, and Rankle (1993). The specification for conditional variance as: (see equation 9H).

σt 2 = w + α i ε2t-1 + γ ε2

t-1 + β j σ2 t-1 ---------- 9H where d1= 1 if εt < 0 , and 0 otherwise as well as for higher order specifications of the TARCH model can be written give by: ( see equation 10H)

σt 2 = w + Σpi =1

α i ε2t-i + Σr

k =1 γ ε2

t-kd t-k + Σq j =1

β j σ2 t-j ---------- 10H

where

σt 2 = variance of TGARCH model w = constant term Σp

i =1 α i ε2

t-i = ARCH term Σr

k =1 γ ε2

t-kd t-k = Threshold ARCH term Σq

j =1 β j σ2 t-j = GARCH term

4.2.6 EGARCH model The EGARCH model or Exponential GARCH model was proposed by Nelson (1991) and the specification for the condition variance give by: ( see equation 11H ).

log( σt 2 ) = w + β log(σ2 t-1 ) + α | ε2t-1 / σ2 t-1 | + γ (ε2

t-1/ σ2 t-1)------- 11H

Where log( σt 2 ) is the log of the condition variance and the present of leverage effect can be tested by the hypothesis that = γ < 0 as well as the impact is asymmetric if γ ≠ 0. For higher order specification of EGARCH model can be written give by: (see equation 12 H ).



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log( σt 2 ) = w + Σq

j =1 βj log(σ2 t-j ) + Σp

i =1 [ α i | εt-i / σ t-i | + γi (ε t-i/ σ t-i) ] ------ 12H

Where w as constant term and log( σt 2 ) is exponential GARCH(p,q) model and higher order specification of EGARCH (p,q) was estimated by the generalized error distribution(GED) can be written give by: (see equation 13H).

log( σt 2 ) = w + Σqj =1

βj log(σ2 t-j ) + Σp i =1

α i [ (εt-i / σ t-i ) - E(ε t-i/ σ t-i) ] + Σr

k =1 γk (ε t-k/ σ t-k) ------ 13H

Where w as constant term and log(σt 2 ) from equation 13H is exponential GARCH(p,q) model was estimated by the generalized error distribution(GED) method. 4.2.7 PARCH model Taylor (1986) and Schwert (1989) introduced the standard deviation GARCH model, where the standard deviation is modeled rather than the variance. This model, along with several other model, is generalized in Ding et al. (1993) with the Power ARCH model (PARCH model) specification. And also the higher order of PARCH model specification can be written give by: (see equation 14H). log( σt

δ ) = w + Σqj =1

βj (σδ t-j ) + Σp i =1

α i [ |εt-i | - γiε t-i)δ ------ 14H Where δ > 0, | γi| ≤ 1 for i = 1,….., n , γi = 0 for all i > n, and n ≤ p and the symmetric model set γi = 0 for all i as well as note that if δ = 2 and γi = 0 for all i, the PARCH model is simply a stand GARCH model specification. The estimates are maximum likelihood estimates which are asymptotically efficient for GARCH(p,d) model. However if the distribution of residuals in not normal distribution, the estimates are still consistent under quasi-maximum likelihood (QML) assumption. The exponential QME is consistent even if the condition distribution of y is not exponential and the exponential therefore QMLE can be written give by : (see equation 15H). ℓ( β ) = Σn

i =1 – log( m)( xj ,β) - (yim (x i , β) ------ 15H



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where ℓ( β ) = the exponential QMLE ( m)( xj ,β) = condition mean yi = time series data β = coefficient of equation And the log likelihood for normal distribution of QMLE also can be written give by equation 16H. ℓ( β ) = ΣN

i =1 {-1/2[( y i – m i)2 /(σ )] – (1/2)log (σ2 ) – (1/2)log(2Π) } --------- 16H

where ℓ( β ) = the normal distribution of QMLE y i = times series data m i = condition mean ( β ) = coefficient of equation 5. The results of the research Two kinds of forecasting methods were employed in this paper for forecasting international tourist arrival to Thailand for 2006-2010. The first group establishes a single variable (the number of international tourist arrivals to Thailand) and includes the following methods: SARIMA, ARIMA, Holt-Winter-Additive, Holt-Winter-Multiplicative, Holt-Winter-No seasonal and Neural network. The second group of forecasting methods establishes more than one variable (the number of international tourist arrivals to Thailand and the growth rate of the country’s industry income). These forecasting methods, include the VAR model, the GMM estimation for time series analysis, the ARCH-GARCH-M model, the ARCH-GARCH model, the TARCH model, the PARCH model and the EGARCH model. 5.1 Forecasting accuracy is based on the Mean Absolutes Percent Error (MAPE) of each method (the method of forecasting from a single variable) The variable was used in these method is the number of international tourist arrivals to Thailand and the table 1 shows forecasting performance accuracy comparisons of the six methods of forecasting international tourist arrivals to Thailand for 2006-2010. Most methods are based on the single variable method of forecasting.



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Table 1: Accuracy comparison in sample for different forecasting models based on the single variable method.

Number Method of forecasting MAPE(%) 1 SARIMA(0,1,1)(0,1,4) 16.73 2 ARIMA(2,1,3) 22.23 3 Holt-Winter-Additive (Three parameter) 22.59 4 Holt-Winter-Multiplicative (Three parameter) 24.30 5 Holt-Winter-No seasonal (Two parameter) 31.31 6 Neural network 32.18

Form: computed Form table 1, the best method to forecasting international tourist arrivals to Thailand during the specified period is SARIMA(0,1,1)(0,1,4). Because the MAPE(%) of this method is lower than the other methods such as ARIMA(2,1,3), Holt-Winter-Additive (three parameter), Holt-Winter-Multiplicative (three parameter), Holt-Winter-No seasonal (two parameter) and Neural network. 5.2 Forecasting accuracy is based on Mean Absolutes Percent Error (MAPE) for each method (more variable) The variables were used in these method such as the number of international tourist arrivals to Thailand and the growth rate income of industry countries in the world. And the table 2 shows the empirical findings of the seven methods for forecast international tourist arrivals to Thailand for 2006-2010. Most method are based on the multi variable method for forecasting. Table 2: An accuracy comparison in sample for different forecasting models based on the multi variable methods for forecasting.

Number Method of forecasting MAPE(%) 1 VAR model 27.26 2 GMM estimation for time series analysis 27.79 3 ARCH-GARCH-M model 28.71 4 ARCH-GARCH model 29.08 5 TARCH model 30.33 6 PARCH model 34.96 7 EGARCH model 39.05

Form: computed Form table 2, the best method for forecasting international tourist arrivals to Thailand during the specified period is the VAR model. Because the MAPE(%) of this method is lower than the other methods such as the GMM estimation for time series analysis, the ARCH-GARCH-M model, the ARCH-GARCH model, the TARCH model, the PARCH model and the EGARCH model.



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5.3 The empirical results of forecasting international tourism demand arrivals to Thailand for 2006-2010 Table 3 presents the results of forecasting by the SARIMA(0,1,1)(0,1,4) model for 2006-2010. Mostly both first quaternary growth rates and second quaternary growth rates in international tourist arrivals to Thailand are negative. And mostly both third quaternary growth rates and fourth quaternary growth rates in international tourist arrivals to Thailand are positive. Furthermore average per year growth rates are positive as well as average per year growth rates equally between 1.40% and 1.50 % during this period. Table 3: Forecasts of quaternary percentage change in international tourist arrivals to Thailand based on the SARIMA(0,1,1)(0,1,4) model during the period 2006-2010

Year Q1 (%)

Q2 (%)

Q3 (%)

Q4 (%)

Average per Year

2006 -6.82 -3.86 10.88 5.69 1.47 2007 -2.03 -0.13 4.11 3.74 1.42 2008 -4.43 -1.92 7.39 4.77 1.45 2009 -3.35 -1.07 5.91 4.36 1.46 2010 -3.94 -1.50 6.75 4.64 1.50

From: computed The table 4 presents the results of forecasting by the VAR model for 2006-2010. Mostly second quaternary growth rates (except both the first quaternary growth rate in 2006 and the second quaternary growth rate in 2007 are negative), the third quaternary growth rate and fourth quaternary growth rate in international tourist arrivals to Thailand are positive. Table 4 : Forecasts of quaternary growth rate percentage change in international tourist arrivals to Thailand based on the VAR model for the period 2006 - 2010.

Year Q1 (%)

Q2 (%)

Q3 (%)

Q4 (%)

Average per Year

2006 1.07 -1.53 5.29 5.04 2.47 2007 -2.17 -0.39 4.59 5.36 1.85 2008 -2.74 0.98 3.76 5.69 1.92 2009 -3.38 2.62 2.76 6.10 2.02 2010 -4.14 4.58 1.62 6.55 2.15

From: computed Mostly first quaternary growth rates in international tourist arrivals to Thailand are negative (except the first quaternary is negative growth). Furthermore the average per year growth rate is positive as well as average per year growth rate equally between 1.90% and 2.50% during this period. The best method of forecasting international tourist arrivals to Thailand based on both the SARIMA(0,1,1)(0,1,4) and VAR model indicates a positive growth rate (average per year) for 2006-2010. Mover over in quaternary three



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and quaternary four based on the two method of forecasting, international tourist arrivals to Thailand is expected to have positive growth (average per year) during this period. 6. The conclusions of research and policy recommendations This paper provides forecasting analysis of international tourist arrivals to Thailand for 2006-2010 based on two categories: (a) Structural Models, in this paper called multi variable forecasting, (b) Trend Extrapolation Models, in this paper called single variable forecasting. The Structural Models or methods used for multiple variable forecasting for predicting the number of international tourist arrival to Thailand for 2006-2010 were the VAR model, the GMM method, the ARCH-GARCH method, the ARCH-GARCH-M method, the TARCH method, the EGARCH method and the PARCH method. The Trend Extrapolation Models or methods of forecasting from a single variable used to forecasts the number of international tourist arrival to Thailand in this period were the Holt-winter method, the ARIMA method, the SARIMA method and the Neural Net work method. The best method of forecasting from Structural Models is the SARIMA(0,1,1)(0,1,4) method because the MAPE value of this method was much lower than for other methods (see table1). And the best method of forecasting from Trend Extrapolation Models was the VAR method because also the MAPE value for this methods was much lower than for other methods (see table 2). The MAPE value was used to look for the best forecasting methods of international tourist arrivals to destination countries in the world (Law and Au, 1999), (Papatheodorou and Song, 2005), (Kon and Turner, 2005). And the SARIMA (0,1,1)(0,1,4) method predicts that in 2010 the number of international tourists arrival to Thailand will be 15,700,656 million (see both appendix A and table 5). Also the VAR method predicts that in 2010 the number of international tourists to Thailand will be 15,985,416 million (see both appendix A and table 6). Therefore the conclusion of this research is that for the next five years, the number of international tourists to Thailand will continue to increase. This result was similar with the results of previous empirical studies of forecasting the international tourist receipts for the world, Asia and Thailand (Papatheodorou and Song, 2005),(Jo Chau Vu and Lindsay W. Turner,2006) which indicate that the number of international tourists in these area will have positive growth rates for 2006-2010. If these results can be generalized for future years, then it suggests that both the Thai government sector and the private tourism industry sector need to prepare for increased numbers of international tourists to Thailand for 2006-2010 and should ensure that there are adequate numbers of hotels, transportation, tourist destinations, tourist police units and airports, and that there is an adequate budget allocated for developing facilities and human resources and for addressing the environmental impact of increased tourism.



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Bibliography G.S Maddala(2002). Introduction To Econometrics third edition Published by John Wiley & Son Ltd India. T. Bollerslev "Generalized Autoregressive Condition Heteroscedasticity" Journal of Econometric vol, 1986, pp 307-236. Andres Papatheodorou and Haiyan Song, (2005). ‘International tourism forecasts: time-series analysis of world and regional data’. Tourism Economics , Vol 9, No 1, pp 11-25. Frechtling, D.C.(1996), Practical Tourism Forecasting, Butterworth-Heinemann, Oxford. Frechtling, D.C.(2001), Forecasting Tourism Demand, Butterworth-Heinemann, Oxford. Hall, Lilien, Sueyoshi, Engle, Johnston and Ellsworth,(2005). Eviews User Guide version 5.1 Econometric Views for Windows and the Macintosh, Quantitative Micro Software Irvine, California and printed in the USA. Krishan K. Kamra, (2006). Economics of Tourism , Kanishka Publishers, Distributors New Delhi-110 002, Printed in India. Mahmoud, E. (1984). ‘Accuracy in forecasting: a survey’, Journal of Forecasting, Vol 3, pp 139-159. Paresh Kumar Narayan,(2005). ‘Testing the unit root hypothesis when the alternative is a trend break stationary process: an application to tourist arrivals in Fiji’.Tourism Economics , Vol 11, No 3, pp 351-364. Rob Law and Norman Au, (1999). ‘A neural network model to forecast Japanese demand for travel to Hong Kong’. Tourism Management , No 20, pp 89-97. Sen Cheong Kon and Lindsay W.Turner, (2005). ‘Neural network forecasting of tourism demand’. Tourism Economics , Vol 11, No 3, pp 301-328. WTO(2003). ‘First WTO World Tourism Barometer shows steadily improving conditions for international tourism’, New s Release, 24 June, World Tourism Organization, Madrid. Jo Chau Vu and Lindsay W. Turner (2006), ‘Regional Data Forecasting Accuracy: The case of Thailand’. Journal of Travel Research, Vol.45,November pp.186-193. R.Engle, “ Autoregressive Conditional Heteroscedasticity with Estimates of the variance of UK. Inflation, ” Econometrica, vol. 50 987-1008,1982.



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Appendix A

Extension experimental results of forecasting international tourist arrivals to Thailand for 2006-2010 based on both the SARIMA method and the VAR method

Table 5. Forecast the number of international tourist arrivals to Thailand for 2006(Q1)- 2010(Q4) based on the SARIMA forecasting method.

Year / Quaternary SARIMA forecasting method

(Million) 2006 Q1 2,977,142.10

Q2 2,862,141.00 Q3 3,173,676.00 Q4 3,354,156.00

Total 12,367,115.10 2007 Q1 3,285,954.00

Q2 3,281,727.00 Q3 3,416,709.00 Q4 3,544,509.00

Total 13,528,899.00 2008 Q1 3,387,561.00

Q2 3,322,602.00 Q3 3,568,173.00 Q4 3,738,279.00

Total 14,016,615.00 2009 Q1 3,613,206.00

Q2 3,574,569.00 Q3 3,785,883.00 Q4 3,950,979.00

Total 14,924,637.00 2010 Q1 3,795,390.00

Q2 3,738,390.00 Q3 3,990,771.00 Q4 4,176,105.00

Total 15,700,656.00 Form computed. Figure 1. Graphical presentation of forecasting international tourist arrivals to Thailand for 2006-2010 based on the SARIMA forecasting method

-500,000.00

1,000,000.001,500,000.002,000,000.002,500,000.003,000,000.003,500,000.004,000,000.004,500,000.00

2006 Q1

Q2 Q3 Q4 2007 Q1

Q2 Q3 Q4 2008 Q1

Q2 Q3 Q4 2009 Q1

Q2 Q3 Q4 2010 Q1

Q2 Q3 Q4

SARIMA forecasting method



30 Form computed .

Table 6. Forecast the number of international tourist arrivals to Thailand during 2006(Q1)- 2010(Q4) based on VAR method.

Year / Quaternary VAR forecasting method

( Million ) 2006 Q1 2,887,912.30

Q2 2,843,776.20 Q3 2,994,270.00 Q4 3,145,155.70

Total 11,871,114.20 2007 Q1 3,076,805.30

Q2 3,064,769.20 Q3 3,205,338.00 Q4 3,376,997.00

Total 12,723,909.50 2008 Q1 3,284,452.10

Q2 3,316,614.90 Q3 3,441,269.00 Q4 3,637,182.00

Total 13,679,518.00 2009 Q1 3,514,418.00

Q2 3,606,444.00 Q3 3,706,075.00 Q4 3,932,221.00

Total 14,759,158.00 2010 Q1 3,769,423.00

Q2 3,941,909.00 Q3 4,005,906.00 Q4 4,268,178.00

Total 15,985,416.00 Form computed.

Figure 2. Graphical presentation of forecasting international tourist arrivals to Thailand for 2006-2010 based on the VAR forecasting method

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From computed.

-500,000.00

1,000,000.001,500,000.002,000,000.002,500,000.003,000,000.003,500,000.004,000,000.004,500,000.00

2006Q1

Q2 Q3 Q4 2007Q1

Q2 Q3 Q4 2008Q1

Q2 Q3 Q4 2009Q1

Q2 Q3 Q4 2010Q1

Q2 Q3 Q4

VAR method



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