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Modelling East Asian exchange rates: a Markov-switching approachGuglielmo Maria Caporale a & Nicola Spagnolo ba Center for Monetary and Financial Economics , South Bank University , London , UKb Department of Economics and Finance , Brunel University , London , UKPublished online: 07 Aug 2006.
To cite this article: Guglielmo Maria Caporale & Nicola Spagnolo (2004) Modelling East Asian exchange rates: a Markov-switching approach, Applied Financial Economics, 14:4, 233-242, DOI: 10.1080/0960310042000201192
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Modelling East Asian exchange rates: a
Markov-switching approach
GUGLIELMO MARIA CAPORALE and NICOLA SPAGNOLO*z
Center for Monetary and Financial Economics, South Bank University, London, UKand zDepartment of Economics and Finance, Brunel University, London, UK
This paper compares the ability of nonlinear and standard linear models to capturethe dynamics of foreign exchanges rates in the presence of structural breaks. Theanalysis is conducted for three East Asian countries, namely Indonesia, South Koreaand Thailand. It is shown that a Markov regime-switching model with shifts in themean and variance (rather than a STAR model) is well suited to capture the non-linearities in exchange rates. Such a model is found to outperform a random walkspecification in terms of both in-sample fitting and out-of-sample forecasting. Inorder to evaluate competing forecasts, accuracy measures based on both the forecasterrors and the variance forecast are used.
I . INTRODUCTION
In the last decade empirical studies on exchange rates have
often focused on nonlinearities in the data generating
mechanism. This has been motivated by their appearance
in some theoretical models (Krugman, 1991; Frankel and
Rose, 1994). A variety of nonlinear univariate exchange
rate models have been considered as a possible alternative
to the widely used linear and random walk processes: time
deformation (Stock, 1987), smooth transition autoregres-
sive (Sarantis, 1999), non-parametric procedures (Diebold
and Nason, 1990; Meese and Rose, 1990), chaos (Hsieh,
1989) and Markov switching models (Engel and Hamilton,
1990) are some of the most commonly used. It is a well-
known fact that nonlinear models generally have very good
in-sample fitting performance, as they are more flexible
than linear models and can more easily capture the usual
features of economics and financial data. However, in the
recent literature many studies have pointed out that non-
linear models do not always produce better forecasts than
linear models. From a forecasting prospective, there
appears to be no clear consensus as to whether allowing
for nonlinearities leads to an improved forecast perfor-
mance (De Gooijer and Kumar, 1992).
Regime-switching models are specifically designed to
capture discrete changes in the economic mechanism that
generates the data. Two main classes of such models are
considered in the literature, namely parametric models
that allow for the transition between the regimes to be
sharp (i.e. Markov-switching (MS) models), and those
where the transition is assumed to be smooth (i.e. smooth
transition autoregressive (STAR) models). The latter type
was estimated by Sarantis (1999) for the real effective
exchange rate in ten major industrial countries, and was
found to outperform MS models in terms of out-of-sample
forecasting. Taylor and Peel (2000) also reported that the
nonlinearity in the dollar–sterling and dollar–mark
exchange rate can be well approximated by an exponential
STAR model.
The alternative approach is to employ Markov regime-
switching models, where the change in regime is itself a
random variable and has to be inferred from the data.
Such models are better suited to capture sharp and discrete
changes in the economic mechanism that generates the
data. The motivation for using them is provided by the
work of Engel and Hamilton (1990), Bekaert and
Hodrick (1993), Engel (1994) and Engel and Hakkio
(1997). All these authors document regime shifts in
*Corresponding author. E-mail: [email protected]
Applied Financial Economics ISSN 0960–3107 print/ISSN 1466–4305 online # 2004 Taylor & Francis Ltd 233
http://www.tandf.co.uk/journalsDOI: 10.1080/0960310042000201192
Applied Financial Economics, 2004, 14, 233–242
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exchange rates, and find that regime switching models pro-vide better in-sample fit and out-of-sample forecasts thanrandom walk specifications.
This class of models is flexible and has interesting prop-erties, with the models being described by a mixture of twoor more distributions. The advantage of such an approachis that it lets the statistical properties of the data suggest theregimes present in the series and also allows the identi-fication of the probabilistic structure of the transitionfrom one regime to another. This study considers a MSspecification which is a simple version of the more generalmodel described by Hamilton (1988, 1989). No dynamicsare included, while both the mean and the variance areallowed to vary according to a hidden Markov chain.Specifically, the exchange rate process is allowed to switchbetween two distributions, one corresponding to a morestable and less volatile period and the other to a less stableand more volatile period. Various evaluation methods ofout-of-sample point and variance forecasts are used. Inaddition to the traditional measures based on forecasterrors such as the mean squared error (MSE), the meanabsolute error (MAE) and Theil’s inequality coefficient, weconsider tests of equal forecast accuracy to assess whetherforecasts from competing models are statistically different.
In brief, we compare the in-sample fitting and out-of-sample forecasting performance of random walk, smoothtransition autoregressive and Markov regime-switchingprocesses when applied to several East Asian nominalexchange rates. MS models should be particularly appro-priate in the case of countries which were hit by a financialcrisis (such as the 1997 East Asia crisis), and experiencedspeculative attacks and severe depreciation. By modellingthe exchange rate as a regime switching process one is ableto take into account the presence of a shift in the condi-tional distribution leading to a well identifiable structuralbreak.1 The remainder of the paper is organized as follows.Section II explains why one might expect a Markov regime-switching model to be particularly appropriate in the caseof foreign exchange markets which are prone to speculativeattacks. Section III introduces the three model specifica-tions. Section IV presents the empirical results and the out-of-sample forecast comparison methods. Section 5 containssummary and conclusions.
II . NONLINEARITIES AND FINANCIALCRISES
The performance of empirical exchange rate models inthe floating period has often been far from satisfactory.One possible reason is that, although there is indeed a
relationship between exchange rates and fundamentals as
predicted by many theories of exchange rate determination,
this involves nonlinearities which have not been taken into
account. For instance, Taylor and Peel (2000) examined the
possibility that deviations of the exchange rate from the
level implied by monetary fundamentals follow a nonlinear
adjustment process, which, they argue, could be owing
to the fact that the costs of arbitrage are governed by
nonlinear factors.
In the case of countries such as the East Asian economies,
which were hit by both a financial and an exchange rate
crisis, one can expect the speed of transition from one
exchange rate regime to another to be much faster than
implied by a STAR model, as the onset of the crisis repre-
sented a major regime shift. It is natural to think, therefore,
that a Markov regime-switching model would be particu-
larly appropriate to capture the features of the data, and to
produce accurate forecasts. In fact, in a recent paper Jeanne
andMasson (2000) showed that the so-called ‘escape clause’
or ‘second generation’ models of financial crises (Obstfeld
1996), which are based on self-fulfilling speculation (as
opposed to fundamentals) and give rise to multiple equilib-
ria, have an obvious empirical counterpart in the Markov-
switching (MS) regime models developed by Hamilton
(1990) and others. They provide a structural interpretation
of such models, showing that regime shifts can be viewed as
jumps between different states of market expectations in an
underlying theoretical model with sunspots (as well as cyclic
or chaotic dynamics for the devaluation expectations).
Specifically, a Markov regime-switching model can be
thought of as a linearized reduced form of structural
form model with sunspots. Assuming that the multiple-
equilibrium approach to currency crises is the correct one,
it is then to be expected that the MS model should outper-
form not only in-sample but also out-of-sample both linear
specifications, such as the random walk model, and also
nonlinear models which do not allow for this kind of sudden
jump from one equilibrium to another. To our knowledge,
although some studies have examined the adequacy of MS
models and compared their performance to that of alterna-
tive modelling approaches in the case of the main industrial
economies (Engel 1994), no such study has been carried out
for the countries for which, we argue, such models are most
naturally suited, namely emerging economies affected by
both financial and currency crises (Jeanne and Masson,
2000, themselves only examine the case of the Fench franc).
Whether one subscribes to a self-fulfilling explanation of
the crisis (as Jeanne and Masson, 2000 do), or to one which
stresses the role of fundamentals (Corsetti et al., 1999) it is
apparent that all East Asian countries underwent a regime
shift. Prior to the 1997 crisis they had experienced a real
1 Some of the countries in the sample had a crawling-peg exchange rate system up to the 1997 crisis; this was then abandoned in favour offree floating. This change corresponds to the regime switch detected in the empirical analysis below.
234 G. M. Caporale and N. Spagnolo
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appreciation, which largely reflected the appreciation of the
US dollar to which they were pegged, and their external
position had substantially deteriorated, owing, at least to
some extent, to this loss in competitiveness. In all cases there
was some form of managed float, though the fluctuation
band was gradually allowed to widen. This predictability
of the exchange rate contributed to a build-up in the
short-term, of unhedged external liabilities. Both financial
and foreign rate markets were clearly vulnerable at the time.
The downturn in exports had been particularly severe in
the case of Thailand. The crisis in fact started with spec-
ulative attacks on the Thai baht, and then spread to the
other countries in the region, which also experienced mas-
sive depreciation, irrespective of whether or not they had a
sizeable current account deficit. The devaluation reflected a
massive increase in the risk premium, which made defend-
ing the exchange rate peg unfeasible. Its effect was to
increase the value of the stock of foreign debt, which in
turn generated fears of insolvency, with governments not
being able to honour the guarantees. The resulting panic
led to the collapse. As Corbett and Vines (1999) stress, the
crucial issue was the size of the devaluation. When the
crisis spread, the economies of the region were not able
to avoid a massive currency depreciation. As a result, the
value of the unhedged foreign borrowings in dollars
increased so dramatically that government bailouts for
the financial system were perceived as too large.
Consequently, the crisis turned into a collapse. The coun-
tries in the region then abandoned the exchange rate peg,
and have been running current-account surpluses most
recently, gradually rebuilding their foreign exchange
reserves.
III . THE MODELS
This section describes the competing models used in the
forecasting exercise. The variables under investigation
are the log changes of foreign exchange rates, EXt ¼
ln½Xt=Xt�1�, where Xt is the foreign exchange rate in US
dollars per unit of foreign currency. First, the standard
random walk is considered which normally provides the
benchmark for all exchange rate models (see Meese and
Rogoff, 1983). Then, a STAR and aMarkov mean-variance
regime-switching model are presented.2
Random walk models
Ever since the seminal paper of Meese and Rogoff (1983), it
has become customary to compare the performance of any
exchange rate model to that of a random walk with driftspecification (RW) of the following form:
�EXt ¼ �0 þ "t, "t � Nð0, �2Þ ð1Þ
with t 2 T
Smooth transition autoregressive models
The idea of smooth transition between regimes (STAR)was first introduced by Bacon and Watts (1971) and popu-larized by Chan and Tong (1986) and Granger andTerasvirtg (1993). A STAR model of order k, for a variableEXt, is specified in the following way:
EXt ¼ �0xt þ h01xtFðEXt�dÞ þ �t ð2Þ
where xt ¼ ð1,EXt�1, . . . ,EXt�kÞ0,� ¼ ð�0,�1, . . . ,�kÞ
0,h1 ¼ ð�0, �1, . . . , �kÞ
0, �t � Nð0, �2Þ, Fð:Þ is the transition
function, EXt�d is the transition variable and d is thedelay parameter. A popular choice for the transitionfunction F(.) , is the logistic function:
FðEXt�dÞ ¼ ½1þ expf��ðEXt�d Þ � cÞg��1ð3Þ
where � defines the speed of transition from one regime tothe other, or smoothness parameter. The parameter c canbe seen as the threshold between the two regimes. When�! 0, the logistic function becomes equal to a constantand when �¼ 0, the STAR model reduces to a linearmodel.
Markov regime-switching models
The Markov regime-switching (MS) models of Hamilton(1988, 1989, 1994) are particularly appropriate in the pres-ence of a sharp shift in the data generating process. EXt ismodelled as being conditionally normal, where the meanand variance both depend on which regime is operative.The regime-switching model considered in this paperallows for shifts in the mean and the variance, that is, forperiods of depreciation and appreciation, and is given by
EXt ¼ �ðstÞ þ �ðstÞ"t, ðt 2 TÞ ð4Þ
�ðstÞ ¼X2i¼1
�ðiÞ1fst ¼ ig, �ðstÞ ¼
X2i¼1
�ðiÞ1fst ¼ ig ð5Þ
where �(i) and �(i) (i¼ 1,2) are real constants, {"t} are i.d.d.errors with E("t)¼ 0 and Eð"2t Þ ¼ 1, and {st} are randomvariables in S¼ {1,2} that indicate the unobserved state ofthe system at date t. Throughout, the regime indicators {st}are assumed to form a homogeneous Markov chain on S
with transition probability matrix P0¼ [pij]2� 2, where
pij ¼ Prðst ¼ jjst�1 ¼ iÞ, i, j 2 S ð6Þ
2A threshold model could also be considered. However, the models examined here are already sufficient to make a significant comparisonbetween the forecasting properties of linear and nonlinear models.
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and pi1 ¼ 1� pi2 ði 2 SÞ.3 It is also assumed that {"t} and{st} are independent. We shall refer to the two state orderMarkov-switching model defined by (4)–(5) as MS. TheMS specification generalizes the standard random walk(RW) model (1) by allowing the variance of the innovation{"t} and the mean to vary between two states according tothe hidden Markov chain {st}. The probability law thatgoverns these regime changes is flexible enough to allowfor a wide variety of different shifts, depending on thevalues of the transition probabilities. For example, valuesof pii ði 2 SÞ not very close to unity imply that structuralparameters are subject to frequent changes, whereas valuesnear unity suggest that only a few regime transitions arelikely to occur in a relatively short realization of theprocess. Also, note that the independence between thesequences {"t} and {st} implies that regime changes takeplace independently of the past history of {EXt}. Theparameter vector �¼ (�(1), �(2), �(1), �(2), p11, p22) is esti-mated by maximum likelihood. The density of the datahas two components, one for each regime, and the log-likelihood function is constructed as a probability weightedsum of these two components. The maximum likelihoodestimation is performed using the EM algorithm describedby Hamilton (1989, 1990).
IV. APPLICATION TO THE EAST ASIANEXCHANGE RATES
This section starts by giving a description of the data andtesting linearity against two specific types of nonlinearity.In-sample performance is measured by log likelihoodvalues and Ljung–Box statistics in a maximum likelihoodframework. Out-of-sample performance is then assessedusing point forecast and variance forecast by meansof several traditional evaluation criteria and accuracymeasures.
Data
Monthly data for three countries are employed: Indonesia,South Korea and Thailand (see top part of Figure 1), overthe period 1970:2–2001:5 for a total of 376 observations.The exchange rates are the local currencies against the USdollar. All data are from International Monetary Fund’sInternational Financial Statistics (IFS). The series beinganalysed are the first difference of the logarithm of theexchange rate. Visual inspection of the series shows thatup until the middle of 1997 volatility is less pronounced,
while thereafter it rises substantially. The Asian crisis, in
fact, began in Thailand in the late spring of 1997 with
sustained speculative attacks on the local currency, and
continued with its flotation in early July 1997. Within
days, speculators had attacked the Indonesian rupiah, the
3 The transition probabilities have not been modelled as a function of other variables. The reason is that the focus is on the ability ofnonlinear models to capture nonlinearities in the data generating mechanism and produce accurate forecasts. The proposed model is nota structural model, but instead a univariate time series representation, whose ability to learn from past events and forecast the futureis analysed.
Fig. 1. Exchange rate returns and filter probabilities of a highmean-variance regime
236 G. M. Caporale and N. Spagnolo
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Korean currency was attacked later on. Table 1 presents a
wide range of descriptive statistics of the three series under
analysis for the full sample and for two subperiods, namely
pre- and post-1997 crisis. Ljung–Box statistics, Q, are also
reported, testing for dependency in the first moment and
LM-ARCH statistics for heteroscedasticity.
Over the whole sample, the mean returns for all coun-
tries are positive. Indonesia, with 0.41%, has the highest
mean return, followed by South Korea with 0.17% and
Thailand with 0.08%. Volatility ranges from 0.97% for
Thailand to 2.55% for Indonesia. It is clear that in the
post-crisis period the East Asian countries experienced
higher volatilities, with a fourfold increase in the case of
Thailand and a twofold increase in the case of Indonesia
and South Korea compared to the pre-crisis sample. In
particular, after the middle of 1997 volatility rose to
6.5% in Indonesia, 2.9% in South Korea and 2.3% in
Thailand. The measures of skewness and excess kurtosis
show that the exchange rates are also heavily skewed and
leptokurtic with respect to the normal distribution.
The Ljung–Box statistics indicate persistent linear
dependency for all three currencies in the whole sample.
In contrast, no signs of persistence are found within the
two subsamples. In the whole sample, there is also evidence
of heteroscedasticity in the squared exchange rate returns.
In contrast, in the two subsamples the null hypothesis ofhomoscedasticity cannot be rejected in any case. Visualinspection of the plot of the data (Figure 1) and thedescriptive statistics both suggest that the empirical distri-butions have been severely influenced by the break whichoccurred in the middle of 1997.
Nonlinearity testing
As a first step, a single regime model is tested against thetwo nonlinear alternatives. It is possible to test directly thenull hypothesis of linearity against the alternative that thedata generating process has been generated according to aSTAR model. When the null hypothesis is valid, H0:�¼ 0,the test statistic is a standard Lagrange multiplier test withan asymptotic x2ð1Þ. Values for the delay parameter d overthe range 1� d� 4 are considered; p-values are reported inTable 2. Using 0.05 as a threshold p-value, one cannotreject the null of linearity in the monthly returns of theexchange rates for all three countries.4
On the contrary, the null hypothesis of linearity againstthe alternative of Markov regime switching cannot betested directly using a standard likelihood ratio (LR) test.This is due to the fact that standard regularity conditionsfor likelihood-based inference are violated under the null
4 It is important to note that this test retains its power as � ! 1, as the smooth transition regression model becomes a switchingregression model (Lukkonen et al. 1988).
Table 1. Descriptive statistics
Whole sample Sub-samples
Country Statistics 1970:2–2001:5 1970:2–1997:7 1997:8–2001:5
Indonesia Mean 0.0041 0.0026 0.0143Std.dev. 0.0255 0.0126 0.0652Skewness 5.2266 7.9854 1.8095Kurtosis 55.224 73.251 9.2959JB 44322 8177.8 98.882Q(10) 59.727 22.586 10.604LM-Arch(10) 64.297 5.3292 4.4261
Korea Mean 0.0017 0.0014 0.0038Std.dev. 0.0118 0.0063 0.0296Skewness 7.5982 6.7621 3.4112Kurtosis 95.256 63.131 18.756JB 136598 52231 552.78Q(10) 94.489 62.621 15.316LM-Arch(10) 18.216 1.6018 1.3159
Thailand Mean 0.0008 0.0004 0.0038Std.dev. 0.0097 0.0057 0.0234Skewness 2.7073 9.5145 0.2447Kurtosis 34.528 109.49 5.7666JB 15989 160776 14.801Q(10) 57.862 8.1208 9.0952LM-Arch(10) 320.34 0.0605 40.668
Note: Q(10) is the Ljung–Box statistics with ten lags while LM-ARCH is the Lagrange multiplierheteroscedasticity test. JB is the Jarque-Bera normality test.
Modelling East Asian exchange rates 237
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hypothesis of linearity, as some parameters are unidentified
and scores are identically zero. However, appropriate test
procedures that overcome the former or both of these
difficulties do exist (Hansen, 1992, 1996; Garcia, 1998).
Hansen’s standardized likelihood ratio test is applied.
This procedure requires evaluation of the likelihood func-
tion across a grid of different values for the transition
probabilities and for each state-dependent parameter. The
value of the standardized likelihood ratio statistics and
related p-values under the null hypothesis (see Hansen,
1996, for details) provides strong evidence in favour of a
Markov mean-variance regime-switching specification for
all the countries.5 Given these results, next we compare the
in-sample and out-of-sample performance of a Markov
regime-switching model and a random walk specification.
Empirical results
The parameter estimates for Indonesia, South Korea and
Thailand together with standard errors, likelihood function
values and diagnostic statistics are presented in Table 3.
Specifically, we test for serial correlation, heteroscedasticity
and normality, in the standardized forecast residuals. The
two competing model residuals are also tested for neglected
nonlinearities. Table 3 reports the p-values of three nonli-
nearity tests, namely the RESET, the BDS and the Neural
test,6 under the null hypothesis that each of the three resi-
duals series is linear. The results confirm those obtained
using the Hansen test, namely it appears that for
Indonesia, South Korea and Thailand the simple random
walk hypothesis as in is not able to capture the features of
the data. There is clear evidence of serial correlation in the
levels, heteroscedasticity and non-normality (see Table 3).
Non-normality and the failure of the neglected nonlinearity
tests for the error term in Equation 1 motivate our use of
a Markov-switching mean-variance model.
In particular, the two-states Markov model (Equation 4)
is considered, where the process is allowed to switch
between two distributions, one corresponding to a low
volatility and the other to a high volatility sample. In par-
ticular, appreciation and depreciation of the local curren-
cies against the US dollar are modelled with volatility being
high during periods of crisis and low during periods of
stability. The likelihood values for this model are well
above the values that were obtained with the linear speci-
fication (see Table 3). The standard errors are all very
small, suggesting that both mean and variance are signifi-
cantly different in each regime. In particular, the high-
variance state is somewhere between 15 times (South
Korea) and 60 times (Indonesia) as volatile as the low-
variance state. Indeed, the two means and variances are
very different across regimes, being much higher in the
‘crisis’ regime than in the other one. In particular, in
the case of Indonesia, the standard deviation of returns
in the low volatility regime is equal to 0.0012 in the pre-
crisis period compared to 0.0740 in the highly volatile post-
crisis sample. The same general pattern emerges for South
Korea and Thailand (see Table 3). Based on the parameter
estimates of the high and low means and variances, the
filter probabilities can be estimated, which are the prob-
ability that each observation is in the high state or the
low state. As the filtering procedure of Hamilton (1990,
1994) shows, the sequence of past exchange rates contains
useful information for the identification of the current state
of the exchange rate. The filtered probabilities of a high
mean-variance state are displayed in the bottom part of
Figure 1. The separation into regimes is very clear-cut,
the probabilities being close to zero or one, and confirms
the impression given by visual inspection of the data. The
transition probabilities appear robust across regimes,
5Note that the two nonlinear models considered in the paper allow one to select the breakpoint endogenously rather than choosing ita priori and then modelling it with a dummy variable. The difference between the two approaches is substantial and makes the nonlinearapproach far more attractive and statistically correct. The point forecasts, in fact, will only depend on the breakpoints inferred from thedata rather that being arbitrarily chosen by the researcher.6 See Lee et al. (1993).
Table 2. Nonlinearity testing
Linearity against STAR model
Indonesia Korea Thailand
Delay1 2.2118 4.7197 4.9695
(0.3312) (0.0944) (0.0833)2 5.9191 2.4917 3.0256
(0.5113) (0.2878) (0.2203)3 6.8974 3.1174 6.1793
(0.0752) (0.3739) (0.1032)4 3.0677 1.7391 13.572
(0.3813) (0.6283) (0.0035)K 2 2 2
Linearity against Markov switching modelStandardized LR test
LR 8.9911 7.9415 8.7653M¼ 0 0.0001 0.0001 0.0001M¼ 1 0.0001 0.0001 0.0001M¼ 2 0.0001 0.0001 0.0001M¼ 3 0.0001 0.0001 0.0001M¼ 4 0.0001 0.0001 0.0001
Note: See Hansen (1996) for details of the test statistic, such as thedefinition of M. p-values are in parentheses. The selectionof the maximum lag order k of the AR was made using SBC.
238 G. M. Caporale and N. Spagnolo
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providing further support for the Markov-switchingspecification. The probability of staying in the high mean-variance regime is 0.72 for Indonesia, 0.69 for South Koreaand 0.88 for Thailand. For all three countries, episodes oflow mean-variance generally appear to last longer thanfinancial turbulence.
Finally, the diagnostic tests show no sign of serial corre-lation, heteroscedasticity and non-normality for this model(see Table 3). Furthermore, the three nonlinearity testsshow no sign of neglected nonlinearity in the estimatedresiduals. On the whole, the empirical results suggest thatthe Markov switching models are able to capture the fea-tures of the data allowing for periods of unusually highmean and volatility through regime switches. They indicatethat splitting the sample is appropriate. In particular,accounting for mean-variance Markov regime switchingeffectively weighs the high-volatility returns less than thelow-volatility ones in the estimation within subsamples.Overall, the two-state Markov switching specificationappears to be appropriate.
Out-of-sample forecast comparison methods
The regime-switching and linear models described abovediffer in their representations of time-varying mean andvolatility. The most common way to evaluate the merits
of comparing models is through out-of-sample forecast
errors "T , h ¼ EXTþh �cEXEXTþh, where cEXEXTþh is the pre-
dicted value and EXTþh is the actual value, with h� 1. In
addition, we also consider the out-of-sample variance fore-
cast defined as s2T , h � E½EX2Tþh� � E½EXTþh�
2. Assuming
one has h-step-ahead forecast errors, where h is the forecast
horizon in months, traditional evaluation criteria are the
mean squared error MSE(h) and the mean absolute error
MAE(h). For the random walk model, an h-month var-
iance forecast, s2T , h, is simply h�2, whereas, for the mean-
variance regime-switching model, the variance forecast is a
function of the regime probabilities, which are updated
prior to each forecast.
Each forecast is then compared with the realized var-
iance over the forecast period, where the realized variance
is given by the sum of the models’ squared residuals.
The last eighteen observations are dropped to which the
forecasts produced by the two competing models are
compared. These are generated as follows. The modelsare estimated up to 1998:11 and then these estimates are
used to generate multi-step ahead forecasts for 1998:12–
2001:5. Simply comparing the values of the MSE(h) and
MAE(h) does not tell us how significant the difference is.
Therefore, a test of equal forecast accuracy is used due to
Diebold and Mariano (1995) which can easily be applied to
examine whether the MSE(h) and theMAE(h) of two alter-
native models, say I and II, are significantly different from
Table 3. In-sample estimation
Indonesia Korea Thailand
Parameters MS RW MS RW MS RW
�0 0.0009 0.0040 0.0008 0.0017 0.0001 0.0007(0.0001) (0.0001) (0.0001) (0.0001) (0.0011) (0.0001)
�1 0.0310 0.0082 0.0059(0.0125) (0.0052) (0.0003)
�0 0.0012 0.0255 0.0021 0.0120 0.0014 0.0099(0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001)
�1 0.0740 0.0332 0.0276(0.0090) (0.0039) (0.0031)
p11 0.7209 0.6977 0.8837(0.0838) (0.0749) (0.0598)
p22 0.9675 0.9566 0.9840(0.0108) (0.0127) (0.0083)
LogLik 1644.39 781.11 1471.42 1043.05 1661.06 1110.54
Diagnostic tests
Q(10) 12.05 64.33 12.73 90.34 9.19 54.11LM-Arch(10) 0.36 59.44 10.22 18.19 0.17 298.04JB 12.456 20918 34.754 62582 29.768 16475RESET 0.654 0.000 0.534 0.012 0.345 0.001NEURAL 0.120 0.000 0.478 0.001 0.567 0.001BDS 0.067 0.000 0.079 0.000 0.101 0.000
Note: The entries in parentheses are the standard errors. Loglik is the log-likelihood. Q(10), LM-ARCH(10) and Jarque–Bera respectively the Ljung–Box statistics with ten lags, the Lagrange Multiplier heteroscedasticity test with ten lags andthe Jarque–Bera normality test. The in-sample estimation period is 1970:2–1998:11 for a total of 346 observations.
Modelling East Asian exchange rates 239
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each other. The loss differential, dT (h), for the h-step fore-cast is
dT ðhÞ ¼ ð"IT , hÞ2� ð"IIT , hÞ
2ð7Þ
for the MSE(h) and
dT ðhÞ ¼ "IT , h
�� ��� "IIT , h
�� �� ð8Þ
for the MAE(h). The null hypothesis of equal forecastaccuracy is E(dT (h))¼ 0.
Another useful criterion which is widely applied in eval-uations of ex-post forecasts is Theil’s inequality coefficient(Theil, 1966), defined as
UðhÞ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=hÞðxTþh � xxTþhÞ
2q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=hÞðxTþhÞ
2q ð9Þ
where xTþh ¼ ð"T , h, s2T , hÞ and h is the number of periods
being forecasted. The scaling of the numerator/denomi-nator is such that U(h) will always fall between 0 and 1.If UðhÞ ¼ 0, xTþh ¼ xxTþh and there is a perfect predic-tion. On the other hand, when U(h)¼ 1 the predictiveperformance of the model is as bad as it could be.
Forecast comparisons are made in the following way.Each time series is composed of Tþh observations, andthe first T observations are used to estimate the linear andnonlinear models. In the two and half years out-of-sampleperiod (from 1998:12 to 2001:5) there are 30 monthsto predict. We generate from all the estimated models 1 toh-step-ahead forecasts. The forecast horizon h has been setequal to 12. A strategy of sequential estimation is employedby rolling over the sample one period at time andhence constructing different forecast series (18) for each
value of h. Table 4 records the results for 1, 2, 5, 10 and
12 step-ahead forecasts. For the MSE(h), MAE(h) and
Theil’s inequality, the results are in terms of ratios (linear/
nonlinear) of the individual loss measures. For the Diebold
Mariano (DM) test, asymptotic p-values are reported.
Table 4 shows that, based on the point forecast compar-
ison, in all three countries no single model dominates
the others, with the Markov switching model predicting
generally better for a short horizon. In particular, for the
nonlinear model, the MSE for one-step-ahead indicates a
32% gain for Indonesia and 38% for Thailand; the gain is
then declining for longer horizons. The results are some-
what different for South Korea, where the linear model
does better for one-and two-step-ahead forecasts, with
the MSE and MAE ratios being smaller than one. The
Theil’s inequality results are in line with those of the two
previous criteria, with none of the two models consistently
outperforming the other. Table 4 also reports the Diebold–
Mariano statistics, the outcomes are rather mixed, but
overall the results indicate that the difference between the
two models is not substantial.
Based on the variance forecast error, the Markov switch-
ing model consistently outperforms the random walk
specification for all three countries. The MSE for one-
step-ahead indicates a 42% gain for Indonesia, 16% for
South Korea and 15% for Thailand. Although the gain
varies for longer horizons, always based on the variance
forecast error, the MSE, the MAE and Theil’s inequality
ratios are always greater than one. The DM test indicates
that the difference between the two models is substantial in
the case of South Korea, whereas it is not so for the other
two countries.
Table 4. Out-of-sample forecasts
h-horizons
Country Point forecast Variance forecast
1 2 5 10 12 1 2 5 10 12Indonesia MSE ratio 1.32 1.18 0.83 1.06 1.02 1.42 1.34 1.34 1.30 1.03
(0.08) (0.31) (0.97) (0.00) (0.04) (0.21) (0.04) (0.30) (0.09) (0.12)MAE ratio 1.40 1.39 1.01 1.01 1.01 1.19 1.44 1.87 1.19 1.07
(0.20) (0.05) (0.33) (0.44) (0.32) (0.18) (0.33) (0.30) (0.08) (0.05)Theil ratio 1.02 1.00 0.89 1.01 1.00 1.38 1.83 1.14 1.11 1.01
Korea MSE ratio 0.99 0.97 1.06 1.01 1.00 1.16 1.36 1.62 1.35 1.28(0.99) (0.04) (0.39) (0.09) (0.56) (0.00) (0.00) (0.00) (0.29) (0.03)
MAE ratio 1.03 0.94 1.21 1.04 1.03 1.07 1.16 1.27 1.41 1.09(1.00) (0.54) (0.22) (0.55) (0.28) (0.00) (0.00) (0.00) (0.00) (0.00)
Theil ratio 1.00 1.17 0.99 1.00 1.00 1.15 1.32 1.53 1.14 1.11Thailand MSE ratio 1.38 1.16 1.06 0.73 0.84 1.15 1.32 1.55 1.87 1.11
(0.00) (0.37) (0.25) (0.93) (0.66) (0.00) (0.12) (0.15) (0.12) (0.56)MAE ratio 1.18 1.32 1.15 0.86 0.96 1.07 1.15 1.25 1.37 1.10
(0.23) (0.06) (0.06) (0.93) (0.91) (0.00) (0.11) (0.13) (0.15) (0.40)Theil ratio 1.15 1.58 1.01 0.99 0.97 1.14 1.30 1.40 1.71 1.05
Note: The p-value for the DM test is reported in parentheses. The out-of sample forecast period is 1998:12–2001:5. For the MSE(h),MAE(h) and Theil’s inequality, the results are in terms of ratios (linear/nonlinear) of the individual loss measures. For the DieboldMariano (DM) test, p-values are reported.
240 G. M. Caporale and N. Spagnolo
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V. CONCLUSIONS
This study has investigated the ability of mean-variance
regime-switching models to capture the time series proper-
ties of exchange rate series that have been subject to a
severe depreciation. Monthly data have been employed
on the local currencies against the US dollar for three
countries, Indonesia, South Korea and Thailand, over the
period 1970:1–2001:5. The crisis which occurred in East
Asia in 1997 led to a massive depreciation of these curren-
cies and represented a major regime shift. As the analysis
shows, standard random walk models are not able to take
into account the structural break which occurred in the
data generating process. Instead, it is more appropriate,
under these circumstances, to employ a Markov regime-
switching model that allows for discrete shifts in the
mean and variance. Such a specification, in fact, provides
a better fit to the data than the competing models, and
captures well the features of the series. The estimated
Markov switching model passes all the diagnostic tests
and provides a satisfactory description of the nonlinearities
found in the data. The results show that there is persistence
of the two states, with the regime characterized by less
volatility exhibiting more persistence. As for the out-
of-sample point forecast results, no single model seems to
completely dominate the others. However, the insults indi-
cate that the mean-variance Markov switching model
reduces the variance forecast error relative to the linear
model. A possible explanation is that the difference
between the two regimes can mainly be put down to a
shift in volatility rather than in the mean, the former not
being taken into account by the point forecast criteria. On
the whole, these results can be interpreted as being consis-
tent with the multiple-equilibrium approach to currency
crises, which emphasizes the role of self-fulfilling expecta-
tions as opposed to fundamentals in explaining crises. In
fact, as shown by Jeanne and Masson (2000), an empirical
model of the type that has been estimated can be seen as a
linearized reduced form of a structural model with multiple
equilibria and sudden jumps from one equilibrium to
another. Surprisingly, to date no empirical studies had
used this framework to model exchange rates in emerging
economies. Our contribution fills this gap.
ACKNOWLEDGEMENTS
Financial assistance from Leverhulme grant F/711/A,
‘Volatility of share prices and the macroeconomy: real
effects of financial crises’, is gratefully acknowledged. We
are also grateful to an anonymous referee and to partici-
pants at the 2000 MMF Meeting, London, 6–8 September
2000, for useful comments.
REFERENCES
Bacon, D. W. and Watts, D. G. (1971) Estimating the transitionbetween two intersecting straight lines, Biometrika, 58,525–34.
Bekaert, C. and Hodrick, R. J. (1993) On biases in the measure-ment of foreign exchange risk premium, Journal ofInternational Money and Finance, 12, 115–38.
Chan, K. S. and Tong, H. (1986) On estimating thresholds inautoregressive models, Journal of Time Series Analysis, 7,179–90.
Corbett, J. and Vines, D. (1999) Asian currency and financialcrises: lessons from vulnerability, crises and collapse, in TheAsian Financial Crises: Causes, Contagion and Consequences(Eds) P. R. Agenos, M. Miller, D. Vines and A. Weber,Cambridge University Press, Cambridge.
Corsetti, G., Pesenti, P. and Roubini, N. (1999) The Asian crisis:an overview of the empirical evidence and policy debate,in The Asian Financial Crises: Causes, Contagion, andConsequences (Eds) P. R. Agenor, M. Miller, D. Vines andA. Weber, Cambridge University Press, Cambridge, pp. 127–163.
De Gooijer, J. G. and Kumar, K. (1992) Some recent develop-ments in nonlinear time series modeling, testing and forecast-ing, International Journal of Forecasting, 8, 135–56.
Diebold, F. X. and Mariano, R. S. (1995) Comparing predictiveaccuracy, Journal of Business and Economic Statistics, 13,253–63.
Diebold, F. X. and Nason, J. A. (1990) Nonparametric exchangerate prediction, Journal of International Economics, 28,315–22.
Engel, C. (1994) Can the Markov switching model forecastexchange rates?, Journal of International Economics, 36,151–65.
Engel, C. and Hakkio, K. (1997) The distribution of exchangerates in the EMS, International Journal of Finance andEconomics, 33, 15–32.
Engel, C. and Hamilton, J. D. (1990) Long swings in the dollar:are they in the data and do the markets know it?, AmericanEconomic Review, 80, 689–713.
Frankel, J. A. and Rose, A. K. (1994) A survey of empiricalresearch on nominal exchange rates, NBER Working Paper,4865.
Garcia, R. (1998) Asymptotic null distribution of the likelihoodratio test in Markov switching models, InternationalEconomic Review, 39, 763–88.
Granger, C. W. J. and Terasvirta, T. (1993) Modelling NonlinearEconomic Relationships, Oxford University Press, Oxford.
Hamilton, J. D. (1988) Rational expectations econometric analy-sis of changes in regime: an investigation of the term struc-ture of interest rates, Journal of Economic Dynamics andControl, 12, 385–423.
Hamilton, J. D. (1989) A new approach to the economic analy-sis of nonstationary time series and the business cycle,Econometrica, 57, 357–84.
Hamilton, J. D. (1990) Analysis of time series subject to changesin regime, Journal of Econometrics, 45, 39–70.
Hamilton, J. D. (1994) Time Series Analysis, Princeton UniversityPress, Princeton, NJ.
Hansen, B. E. (1992) The likelihood ratio test undernonstandard conditions: testing the Markov switchingmodel of GNP, Journal of Applied Econometrics, 7, 61–82.
Hansen, B. E. (1996) Erratum: The likelihood ratio testunder nonstandard conditions: testing the Markovswitching model of GNP, Journal of Applied Econometrics,11, 195–8.
Modelling East Asian exchange rates 241
Dow
nloa
ded
by [
Uni
vers
ity o
f N
orth
Car
olin
a] a
t 12:
01 1
2 N
ovem
ber
2014
Hsieh, D. A. (1989) Testing for nonlinear dependence in foreignexchange rate, Journal of Business, 62, 339–68.
Jeanne, O. and Masson, P. (2000) Currency crises, sunspotsand Markov-switching regimes, Journal of InternationalEconomics, 50, 327–50.
Krugman, P. (1991) Target zones and exchange rate dynamics,Quarterly Journal of Economics, 106, 669–82.
Lee, T.-H., White, H. and Granger, C. W. J. (1993) Testing forneglected nonlinearity in time series models: a comparisonof neural network methods and alternative tests, Journalof Econometrics, 56, 269–90.
Lukkonen, R., Saikkonen, P. and Terasvirta, T. (1988) Testinglinearity against smooth transition autoregressive models,Biometrika, 75, 491–9.
Meese, R. A. and Rogoff, K. (1983) Empirical exchange ratemodels of the seventies: do they fit out of sample?, Journalof International Economics, 14, 3–12.
Meese, R. A. and Rose, A. K. (1990) Nonlinear, nonparametric,nonessential exchange rate estimation, The AmericanEconomic Review, 80, 192–6.
Obstfeld, M. (1996) Models of currency crises with self-fulfillingfeatures, European Economic Review, 40, 1037–47.
Sarantis, N. (1999) Modeling non-linearities in real effectiveexchange rates, Journal of International Money and Finance,18, 27–45.
Stock, J. H. (1987) Measuring business cycle time, Journal ofPolitical Economy, 95, 132–54.
Taylor, M. P. and Peel, D. A. (2000) Nonlinear adjustment, long-run equilibrium and exchange rate fundamentals, Journal ofInternational Money and Finance, 19, 33–53.
Theil, H. (1966) Applied Economic Forecasts, North-Holland,Amsterdam.
242 G. M. Caporale and N. Spagnolo
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