4th Annual BSP‐UP Professorial Chair Lectures 21 – 23 February 2011 

Bangko Sentral ng Pilipinas Malate, Manila 

 

Lecture No. 3  

Forecasting Exchange Rates in Stable and Turbulent Times: The Case of the Philippine Peso–US Dollar Rate 

 by   

Dr. Joel Yu BSP‐UP Centennial Professor 

of Finance    

The author acknowledges the support of the Bangko Sentral ng Pilipinas. The views expressed in this paper do not reflect the views of the BSP.

This Version

1 February 2011

Forecasting Exchange Rates in Stable and Turbulent Times: The Case of the Philippine Peso-US Dollar Rate

Joel C. Yu

Abstract

This paper evaluates the short-term predictive accuracy of empirical models of the Philippine

Peso to US dollar rate. Out-of-sample forecasts were generated from alternative models in the

period 2006-2010, which includes sub-periods of relative stability and turbulence. The

models were evaluated using mean absolute error (MAE), mean square error (MSE), and

mean absolute percentage error (MAPE). Using the Diebold-Mariano statistic, tests were

made to determine whether the predictive accuracy of an empirical model is significantly

different from that of a random walk model.

Correspondence:

Joel C. Yu

Associate Professor College of Business Administration

University of the Philippines

UP Campus, Diliman

Quezon City Philippines

Email: joel.yu@up.edu.ph

Tel: +63 (02) 928-4571

1

Forecasting Exchange Rates in Stable and Turbulent Times: The Case of the Philippine Peso-US Dollar Rate

Joel Yu

1. Introduction

Towards the end of each year, researchers and analysts have their hands full in

making forecasts on key economic variables; Among these variables is the foreign exchange

rate. Exchange rate projections are vital to businessmen, especially those who are exposed to

foreign exchange risks. These projections are equally important to policy makers who use

them as inputs in their policy decisions. To households, particularly those who partly depend

on the remittances of a household member who works abroad, projections on exchange rates

are considered in estimating income and in planning family expenditures.

How well do these forecasts fare? Do they consistently hit the mark?

About 30 years ago, Meese and Rogoff, (1983), henceforth referred to as MR, asked a

similar question: Do exchange rate models of the seventies fit out of sample? They evaluated

empirical exchange rate models of the seventies by comparing the out-of-sample forecasting accuracy of structural and time series models of major currencies. Forecasts of structural

models were made using the actual values of the future explanatory variables to eliminate errors that originate from wrong assumptions on these variables. The results of the MR

experiment show that none of the empirical exchange rate models does better than the simple random walk model at any forecast horizon considered in the study.

What are the possible reasons for the disappointing performance of empirical foreign

exchange rate models, particularly the structural models? Since these models benefit from the

elimination of the uncertainty in the explanatory variables, MR made the following

conjectures on the cause of their poor forecasting performance: simultaneous equation bias,

sampling error, stochastic movements in the true underlying parameters, or misspecification.

They also hinted on the possibility of non-linearity in the underlying models.

The MR experiment brought forth a major stream of research in empirical foreign

exchange rate modeling. On the whole, subsequent research failed to come up with an

empirical exchange rate model that can outperform the random walk model. The only major

qualification is that models can outperform the forecasts of a random walk model in longer

time horizons of three to four years (Mark, 1995).

Despite the mounting research on exchange rate models, there are incessant efforts to qualify the results of the MR experiment. Some would consider different currencies (e.g.,

focusing on a particular currency or groups of currencies like those of emerging economies and the so-called commodity currencies). Others would refine the methods in estimating the

models to account for such things as non-linearity in the models and stochastic movements in the underlying parameters. There are also those which qualify the approach used in

comparing the predictive accuracy of the different models.

2

This paper adds to the research that seeks to qualify the results of the MR experiment.

It addresses the question on how the random walk model compare with alternative models in out-of-sample short-term forecasts for a period that includes sub-periods of relative stability

and turbulence. During such times, it is expected that the magnitude of errors of a random walk model will rise due to the increased volatility in exchange rates. How do empirical

exchange rate models compare to the random walk model during such period?

This paper limits itself to the exchange rate between the Philippine peso and the US Dollar. The out-of-sample forecast period extends from January 2006 to November 2010.

This period includes fairly stable sub-periods and turbulent times starting from September

2008 when the Lehmann Brothers declared bankruptcy and precipitated an increased

volatility in exchange rates.

Section two of the paper presents a brief review of the empirical models of exchange

rates, the models that are considered in the paper, and the data used in the experiment.

Section three presents the methodology in comparing the forecasting accuracy of the different

models. Section four shows the results and analysis. Section five presents some concluding

remarks.

2. Foreign Exchange Rate Models

2.1. Model Specification and Estimation

One of the most basic models of foreign exchange rates is the flexible-price monetary

model. This model assumes monetary equilibrium in both the domestic and foreign economies. Hence,

hrkypms −+= (1)

******

rhykpms −+= (2)

where ms is the logarithm of money supply, y is the logarithm of real output, r is the interest

rate, and k and h are positive parameters. The variables with asterisk refer to the variables in

foreign economy; those without the asterisk correspond to the variables in the domestic

economy.

The model also assumes the purchasing power parity. Premised on the law of one

price, the relative version of the purchasing power parity claims that the differential rate of inflation determines the change in exchange rates in the long run. Thus,

*pps −= (3)

where s is the logarithm of the exchange rate (expressed as the price of a foreign currency in

terms of the domestic currency, i.e, direct quote), p is the logarithm of the domestic price

level, and p* is the logarithm of the foreign price level.

3

Together with the monetary equilibrium in both the domestic and foreign economies,

the relative purchasing power parity establishes the following relationship:

)()()( *****rhhrykkymms −+−−−= (4)

Equation 4 shows a positive relationship between exchange rate and the differential in

the growth of money supply. An increase in money supply results in an increased demand in

foreign goods, which, in turn, increases the demand for foreign currency. Ultimately, the rise

in domestic money supply leads to a depreciation in the domestic currency.

The link between the domestic supply of money and the exchange rate may also be

understood in the context of the effects of money supply on the aggregate demand for

domestic goods. A rise in money supply stimulates the demand for domestic goods. Without a

corresponding rise in aggregate supply, this results in a rise in prices and creates pressure for

a depreciation of the domestic currency.

Equation 4 also provides that a rise (fall) domestic output and a decrease (increase) in interest rate results in an appreciation of the domestic currency. These variables affect the

exchange rate through their impact on inflation. The monetary equilibrium indicates that a rise in output and a decline in interest rates lower inflation. Based on the purchasing parity

condition, lower domestic inflation results in an appreciation in the domestic currency.

A main drawback of the flexible-price monetary model is the lack of empirical

support for it especially in the short term. This is so because the relative purchasing power

parity on which the model is premised is a long-term relationship. Besides, the model rests on

the assumption that the demand for money is stable over time. The model also requires a

variable for real output, which, for short-term models, is quantified using the volume of

production index. In the Philippines, this data has a break in the mid 90’s and only covers the

manufacturing sector. This adds a complication in estimating the parameters of an empirical

peso-US dollar rate model based on the flexible-prices monetary model.

An alternative foreign exchange rate model is Frankel’s real interest differential model

(Frankel, 1979) which builds on the uncovered interest parity (UIP). In its logarithmic form,

the UIP establishes the following relationship:

*rrsse −=− (5)

Where se is the expected exchange rate and sse − is the expected rate of change in the

exchange rate. This expectation is defined as:

)()( *ppssss

e −+−=− θ (6)

where s is the long-run equilibrium rate of exchange and θ is a positive parameter.

Together, the UIP and specification of the expected rate of depreciation yield:

[ ])()(1 **

prprss −−−=−θ

(6)

4

Equation 6 states that changes in exchange rates around the equilibrium level, s , is

proportionate to the real interest rate differential. When the exchange rate is equal to its long-

run equilibrium level, then the real interest rates in both the domestic and foreign economies

are in equality. If the domestic economy maintains a tight monetary policy, the domestic

interest rate rises and results in an appreciation of the domestic currency.

Estimating structural models of exchange rates confronts a practical problem in

identifying the appropriate data to represent the variables. Some of these variables cannot be

measured directly and the data that are traditionally used to represent them suffer from significant measurement errors. To address this issue, Solnik (1987) proposed the use of

financial prices in testing exchange rate models.

Noting the proposal of Solnik, this paper adopts the following specification of an empirical model of exchange rates:

tmtmtttt RRrrs εβββ +−+−+= )()( *

2

*

10 (7)

where )( *

mtmt RR − is the differential stock market returns between the domestic and foreign

economies. Stock returns have been shown to provide a good indication on the level of economic activity (Solnik, 1987). Employing market portfolio returns provides the benefit of

avoiding measurement errors and the complexities brought about by the revisions in the traditional data used to represent variables such as output.

The error term in equation (7), tε , is conventionally assumed to have a zero mean

and constant variance. In such case, the parameters may be estimated using ordinary least

squares. However, if the error term has a time varying variance, h2, it is more appropriate to

estimate a model for it. A parsimonious GARCH(1,1) given in equation (8) will also be

considered in this study.

12

2

110

2

−− ++= tthh εγγγ (8)

Finally, the parameters of equation (7), iβ , need not be fixed. These parameters may

change due to variations in the magnitude of effects of the explanatory variables on the exchange rates. In this paper, these parameters are assumed to change based on a non-

observable state, RGM. Assuming there are two states, equation (7) may be expressed as follows:

=+−+−+

=+−+−+=

2RGM if ,)()(

1RGM if ,)()(

t2

*

22

*

2120

t1

*

12

*

1110

tmttmtt

tmttmtt

tRRrr

RRrrs

εβββ

εβββ (9)

In this specification, the non-observable state, RGMt, is assumed to follow an ergodic

first-order Markov chain process described by following transition probabilities

5

( ) ijtt piRGMjRGM === − 1Pr , where∑=

=2

1j

ij 1p . (10)

These transition probabilities are generally summarized in a transition matrix P given by:

=

2221

1211

pp

ppP (11)

In sum, the parameters of the structural model presented in equation (7) will be estimated under three different assumptions: one, the error term has a constant variance; two,

the error term has a time-varying variance that is characterized by a GARCH(1,1) process; and three, the parameters change between two unobservable states, RGM. The statistics of the

first two empirical models are estimated using EVIEWS while those of the third model are estimated using the Krolzig’s (1997) Ox program for markov-switching models.

The three approaches in estimating the parameters of the structural model will also be

employed in estimating those of an AR(1) model for the peso to US dollar rates. Together

with the three structural models, these three time series models complete the six models

considered in this paper.

2.2. Data

This study used monthly data from January 1990 to November 2010. The data on

exchange rates are the monthly average rates published by the Bangko Sentral ng Pilipinas

(BSP) in its website. It is also the source of the data on interest rates which is represented by

the 90-day treasury bill rate. The stock market returns in the Philippines are measured by the

return on the portfolio of stocks that comprise the PSE index.

Data on the interest rates and stock returns in the US were sourced from the Federal Reserve Economic Database, FRED, of the Federal Reserve Bank of St. Louis. The interest

rate in the US is represented by the secondary market rate of the US three-month treasury bill. The stock market return in the US is measured by the return on the S&P 500.

3. Comparing Predictive Accuracy

Initially, the models were estimated using data from January 1990 to December 2005.

Forecasts were generated for one-, three-, six-, and twelve-month horizons. The different

forecast horizons were considered to allow comparison among the models’ forecasting ability

at different horizons.

After generating the forecasts, the models are re-estimated with the next data point

added in the sample period. The model is then re-estimated to mimic a “diligent” forecaster

who updates the parameter estimates of the model before making the next set of forecasts.

Similar to the original MR experiment, the actual values of the explanatory variables

of the structural model were used in forecasting. As mentioned earlier, this gets rid of forecast

errors that arise from errors in the assumed values of the explanatory variables.

6

In comparing the predictive accuracy of the alternative models, we initially use the following traditional measures: mean absolute error (MAE), mean square error (MSE), and

mean absolute percentage error (MAPE).

kT

SS

MAE

kT

t

F

kt

A

kt

−

−

=∑

−

=

++

0 (12)

( )

kT

SS

MSE

kT

t

F

kt

A

kt

−

−

=∑

−

=

++

0

2

(13)

−

−= ∑

−

= +

++kT

tA

kt

F

kt

A

kt

S

SS

kTMAPE

0

1 (14)

where k is the forecast horizon (i.e., k = 1, 3, 6, 12)

In addition, the paper employs the Diebold-Mariano (DM) statistic for comparing

predictive accuracy:

Tf

dDM

d /)0(ˆ2π= (15)

where d is the sample mean loss differential between two alternative forecast methods and

Tfd /)0(ˆ2π is the variance. Thus,

∑=

=T

t

tdT

d1

1 (16)

where the variable td is the loss differential at time t. This loss differential is the difference

between the loss function of alternative forecasting models 1 and 2, i.e., )()( 21 ttt egegd −=

and )( iteg is the loss function of model i. In this paper, the loss function is defined as the

MAE. The variance of the loss function is estimated using the method of Newey-West for a heteroschedasticity and autocorrelation consistent estimator of asymptotic variance.

The DM statistic is used to test the null hypothesis that the expected loss differential

is zero, i.e., the expected loss function of two competing models are equal.

7

4. Results

Table 1 presents the MAE, MSE, and MAPE of the different models. It also shows

that rank of the models based on the three measures. It can be noted that the random walk and the parsimonious AR(1) model dominates the structural models in all forecast horizons

considered in the study. Such is the case even if the structural models benefit from eliminating the forecast errors that originate from wrong assumptions on the explanatory

variables. In this sense, the results of this study are no different from those of the MR experiment which were done three decades ago.

Table 2 shows further evidence that the dominance of the random walk model over

the structural models is, for most part, statistically significant. Except for the 12-month ahead

forecasts of the GARCH model and the Markov-switching model, all the DM statistics are

significantly different from zero.

The graphs in Chart 1 plot the loss differential of the structural models compared to

the random walk model. It is worth noting that, in most cases, the loss differential is above

zero. This indicates that the error of the random walk model is usually less than that of the

structural models. The only positive aspect that can be noted in the out-of-sample forecasts of

the structural models is the decline in the loss differential of the Markov-switching model

during the turbulent months starting from September 2008. However, this is not enough to

eclipse the overall performance of the random walk model.

As regards the time series models, the random walk was able to consistently dominate the AR(1) model which was estimated using ordinary least squares. (Refer to Table 1.) The

AR(1) model with GARCH(1,1) error term and the one with markov-switching parameters are not dominated by the random walk model. However, the advantage of these models are

not statistically significant. (Refer to Table 2.)

It is interesting to note from Chart 2 that, in a number of cases, the out-of-sample

forecasts of the time series models gained an upper hand over the random walk model during

the crisis that started in late 2008. This is specially true for the markov-switching model.

5. Concluding Remarks

This paper sought to qualify the MR experiment by examining the performance of

empirical exchange rate models in out-of-sample forecasts during periods that contain sub-

periods of relative stability and turbulence. The results show that the structural models are

dominated by the random walk model in all four forecast horizons considered in this study.

However, this cannot be said about a parsimonious AR(1) model whose error term is

assumed to follow a GARCH(1,1) process and a similar model that is assumed to have markov-switching parameters. The gains of the latter model over the random walk were

obtained during the crisis period that started in September 2008. This suggests that the recognition of instability in the parameter estimates bears fruit in short-term out-of-sample

forecasts.

8

6. References

Diebold, F. and Mariano, R. (1995 ) Comparing Predictive Accuracy, Journal of Business and Economic Statistics, 13, 253-265.

Engel, C (1994) Can the Markov switching model forecast exchange rates?, Journal of

International Economics 36, 151-165.

Frommel M., et. al. (2005) Markov switching regimes in a monetary exchange rate model,

Economic Modelling 22, 485-502.

Hamilton, J., (1989) A new approach to the economic analysis of non-stationary time series

and the business cycle, Econometrica, 57, 357-384.

Kim and Nelson (1999) State Space Models with Regime Switching, MIT Press.

Krolzig, H.-M. (1997) Markov-Switching Vector Autoregressions. Modelling, Statistical

Inference and Application to Business Cycle Analysis, Lecture Notes in Economics and

Mathematical Systems, Volume 454, Berlin: Springer.

Krolzig, H.-M. and Sensier M. (2000) A Disaggregated Markov-Switching Model of the Business Cycle in UK Manufacturing, Manchester School 68 (4), 442- 460.

Mark, N. (1995) Exchange Rates and fundamentals: Evidence on Long Horizon Predictability,

American Economic Review, 85-1, 201-218

Meese, R. and Rogoff, K. (1983) Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?, Journal of International Economics, 14, 3-24

Rogoff, K. (2001) The failure of empirical exchange rate models: no longer new, but still true,

Economic Policy Web Essay 1.

Solnik, B. (1987) Using Financial Prices to Test Exchange Rate Models: A Note, Journal of

Finance, 42, 141-149.

9

Table 1

Predictive Accuracy

Levels Rank

1-mo 3-mo 6-mo 12-mo 1-mo 3-mo 6-mo 12-mo

1. MAE

Random Walk Model 0.0148 0.0330 0.0508 0.0876 1 3 3 3

1.1. Structural Models

OLS 0.1108 0.1152 0.1237 0.1374 7 7 7 7

GARCH 0.0995 0.1096 0.1152 0.1108 6 6 6 5

MS 0.0889 0.0955 0.1036 0.1212 5 5 5 6

1.2. Time Series Models

OLS 0.0152 0.0352 0.0569 0.0991 4 4 4 4

GARCH 0.0148 0.0327 0.0505 0.0873 2 2 2 2

MS 0.0150 0.0322 0.0479 0.0872 3 1 1 1

2. MSE

Random Walk Model 0.0003 0.0016 0.0039 0.0100 2 3 2 1

2.1. Structural Models

OLS 0.0165 0.0178 0.0198 0.0235 7 7 7 7

GARCH 0.0142 0.0160 0.0166 0.0156 6 6 6 5

MS 0.0119 0.0137 0.0164 0.0228 5 5 5 6

2.2. Time Series Models

OLS 0.0003 0.0018 0.0044 0.0122 4 4 4 4

GARCH 0.0003 0.0016 0.0040 0.0104 1 2 3 3

MS 0.0003 0.0016 0.0036 0.0102 3 1 1 2

3. MAPE

Random Walk Model 0.0038 0.0086 0.0133 0.0088 1 3 3 1

3.1. Structural Models

OLS 0.0289 0.0301 0.0323 0.0360 7 7 7 7

GARCH 0.0258 0.0285 0.0300 0.0290 6 6 6 5

MS 0.0233 0.0250 0.0271 0.0318 5 5 5 6

3.2. Time Series Models

OLS 0.0040 0.0092 0.0149 0.0260 4 4 4 4

GARCH 0.0039 0.0085 0.0132 0.0229 2 2 2 3

MS 0.0039 0.0084 0.0125 0.0228 3 1 1 2

10

Table 2

Predictive Accuracy

Forecast Horizon

1 3 6 12

I. Structural Models

OLS DM 0.09603 0.08215 0.07293 0.04981

prob 0.00000 0.00000 0.00000 0.00020

GARCH DM 0.08477 0.07661 0.06441 0.02324

prob 0.00000 0.00000 0.00020 0.14310

MS DM 0.07414 0.06246 0.05280 0.03365

prob 0.00000 0.00010 0.00140 0.11150

II. Time Series Models

OLS DM 0.00047 0.00218 0.00616 0.01152

prob 0.09320 0.03940 0.01050 0.03990

GARCH DM 0.00006 -0.00031 -0.00033 -0.00025

prob 0.62050 0.55400 0.77300 0.92350

MS DM 0.00026 -0.00083 -0.00285 -0.00042

prob 0.43000 0.36490 0.27900 0.94090

Notes:

The benchmark loss function is that of the random walk model.

The fonts in bold indicate that the DM is statistically significant at 10% level.

11

Chart 1

Loss Differential for Structural Models One month Three months Six months Twelve months

OL

S

-.04

.00

.04

.08

.12

.16

.20

.24

.28

2006 2007 2008 2009 2010

Model D

-.10

-.05

.00

.05

.10

.15

.20

.25

2006 2007 2008 2009 2010

Model D

-.10

-.05

.00

.05

.10

.15

.20

.25

2006 2007 2008 2009 2010

Model D

-.15

-.10

-.05

.00

.05

.10

.15

.20

2006 2007 2008 2009 2010

Model D

GA

RC

H

-.05

.00

.05

.10

.15

.20

.25

2006 2007 2008 2009 2010

Model E

-.05

.00

.05

.10

.15

.20

.25

2006 2007 2008 2009 2010

Model E

-.12

-.08

-.04

.00

.04

.08

.12

.16

.20

2006 2007 2008 2009 2010

Model E

-.15

-.10

-.05

.00

.05

.10

.15

2006 2007 2008 2009 2010

Model E

Mar

kov

-Sw

itch

ing

-.05

.00

.05

.10

.15

.20

.25

2006 2007 2008 2009 2010

Model F

-.05

.00

.05

.10

.15

.20

.25

2006 2007 2008 2009 2010

Model F

-.15

-.10

-.05

.00

.05

.10

.15

.20

.25

2006 2007 2008 2009 2010

Model F

-.15

-.10

-.05

.00

.05

.10

.15

.20

2006 2007 2008 2009 2010

Model F

Note: Loss differential is defined as )()( RW

t

i

tt egegd −= where )( i

teg is the loss function of model i defined as the mean absolute error.

12

Chart 2

Loss Differential:

Time Series Model One month Three months Six months Twelve months

OL

S

-.003

-.002

-.001

.000

.001

.002

.003

.004

2006 2007 2008 2009 2010

Model A

-.008

-.004

.000

.004

.008

.012

2006 2007 2008 2009 2010

Model A

-.015

-.010

-.005

.000

.005

.010

.015

.020

2006 2007 2008 2009 2010

Model A

-.03

-.02

-.01

.00

.01

.02

.03

.04

2006 2007 2008 2009 2010

Model A

GA

RC

H

-.0016

-.0012

-.0008

-.0004

.0000

.0004

.0008

.0012

.0016

2006 2007 2008 2009 2010

Model B

-.006

-.004

-.002

.000

.002

.004

.006

2006 2007 2008 2009 2010

Model B

-.010

-.005

.000

.005

.010

2006 2007 2008 2009 2010

Model B

-.016

-.012

-.008

-.004

.000

.004

.008

.012

.016

2006 2007 2008 2009 2010

Model B

Mar

kov

-Sw

itch

ing

-.008

-.004

.000

.004

.008

.012

2006 2007 2008 2009 2010

Model C

-.03

-.02

-.01

.00

.01

.02

.03

2006 2007 2008 2009 2010

Model C

-.05

-.04

-.03

-.02

-.01

.00

.01

.02

.03

2006 2007 2008 2009 2010

Model C

-.10

-.08

-.06

-.04

-.02

.00

.02

.04

2006 2007 2008 2009 2010

Model C

Note: Loss differential is defined as )()( RW

t

i

tt egegd −= where )( i

teg is the loss function of model i defined as the mean absolute error.