Journal of International Money and Finance
24 (2005) 1150e1175
www.elsevier.com/locate/econbase

Empirical exchange rate models of thenineties: Are any ﬁt to survive?
Yin-Wong Cheung a,*, Menzie D. Chinn b,
Antonio Garcia Pascual cab

Department of Economics, E2, University of California, Santa Cruz, CA 95064, USA
LaFollette School of Public Aﬀairs and Department of Economics, University of Wisconsin
and NBER, 1180 Observatory Drive, Madison, WI 53706, USA
c
International Monetary Fund, 700 19th Street NW, Washington, DC 20431, USA

Abstract
We re-assess exchange rate prediction using a wider set of models that have been proposedin the last decade: interest rate parity, productivity based models, and a composite speciﬁcation. The performance of these models is compared against two reference speciﬁcations e purchasing power parity and the sticky-price monetary model. The models are estimated inﬁrst-diﬀerence and error correction speciﬁcations, and model performance evaluated at forecast horizons of 1, 4 and 20 quarters, using the mean squared error, direction of change
metrics, and the ‘‘consistency’’ test of Cheung and Chinn [1998. Integration, cointegration,and the forecast consistency of structural exchange rate models. Journal of International
Money and Finance 17, 813e830]. Overall, model/speciﬁcation/currency combinations thatwork well in one period do not necessarily work well in another period.
Ó 2005 Elsevier Ltd. All rights reserved.
JEL classiﬁcation: F31; F47
Keywords: Exchange rates; Monetary model; Productivity; Interest rate parity; Purchasing power parity;
Forecasting performance* Corresponding author. Tel.: C1 831 459 4247; fax: C1 831 459 5900.
E-mail address: cheung@ucsc.edu (Y.-W. Cheung).
0261-5606/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jimonﬁn.2005.08.002

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1151

1. Introduction
The recent movements in the dollar and the euro have appeared seemingly inexplicable in the context of standard models. While the dollar may not have been ‘‘dazzling’’ e as it was described in the mid-1980s e it has been characterized as overly‘‘darling.’’1 And the euro’s ability to repeatedly confound predictions needs little
re-emphasizing.
It is against this backdrop that several new models have been forwarded in thepast decade. Some explanations are motivated by ﬁndings in the empirical and theoretical literature, such as the correlation between net foreign asset positions and realexchange rates and those based on productivity diﬀerences. None of these models,
however, have been subjected to rigorous examination of the sort that Meese andRogoﬀ conducted in their seminal work, the original title of which we have appropriated and amended for this study.2
We believe that a systematic examination of these newer empirical models is long
overdue, for a number of reasons. First, while these models have become prominent
in policy and ﬁnancial circles, they have not been subjected to the sort systematic
out-of-sample testing conducted in academic studies. For instance, productivity
did not make an appearance in earlier comparative studies, but has been tapped
as an important determinant of the euroedollar exchange rate (Owen, 2001; Rosenberg, 2000).3
Second, most of the recent academic treatments’ exchange rate forecasting performance relies upon a single model e such as the monetary model e or some otherlimited set of models of 1970s’ vintage, such as purchasing power parity or real interest diﬀerential model.
Third, the same criteria are often used, neglecting alternative dimensions of model
forecast performance. That is, the ﬁrst and second moment metrics such as mean error and mean squared error are considered, while other aspects that might be ofgreater importance are often neglected. We have in mind the direction of change eperhaps more important from a market timing perspective e and other indicators offorecast attributes.
In this study, we extend the forecast comparison of exchange rate models in several dimensions.
 Five models are compared against the random walk. Purchasing power parity is
included because of its importance in the international ﬁnance literature and the1

Frankel (1985) and The Economist (2001), respectively.
Meese and Rogoﬀ (1983) was based upon work in ‘‘Empirical exchange rate models of the seventies:
are any ﬁt to survive?’’ International Finance Discussion Paper No. 184 (Board of Governors of the Federal
Reserve System, 1981).
3
Similarly, behavioral equilibrium exchange rate (BEER) models e essentially combinations of real interest diﬀerential, nontraded goods and portfolio balance models e have been used in estimating the‘‘equilibrium’’ values of the euro. See Bank of America (Yilmaz, 2003), Bundesbank (Clostermann and
Schnatz, 2000), ECB (Schnatz et al., 2004), and IMF (Alberola et al., 1999). A corresponding study forthe dollar is Yilmaz and Jen (2001).
2

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Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

fact that the parity condition is commonly used to gauge the degree of exchange
rate misalignment. The sticky-price monetary model of Dornbusch and Frankel
is the only structural model that has been the subject of previous systematic analyses. The other models include one incorporating productivity diﬀerentials, aninterest rate parity speciﬁcation, and a composite speciﬁcation incorporating
a number of channels identiﬁed in diﬀering theoretical models.
 The behavior of US dollar-based exchange rates of the Canadian dollar, British
pound, Deutsche mark and Japanese yen are examined. To insure that our conclusions are not driven by dollar speciﬁc results, we also examine (but do not report) the results for the corresponding yen-based rates.
 The models are estimated in two ways: in ﬁrst-diﬀerence and error correction
speciﬁcations.
 Forecasting performance is evaluated at several horizons (1-, 4- and 20-quarter
horizons) and in two sample periods (post-Louvre Accord and post-1982).
 We augment the conventional metrics with a direction of change statistic and the‘‘consistency’’ criterion of Cheung and Chinn (1998).
Before proceeding further, it may prove worthwhile to emphasize why we focus
on out-of-sample prediction as our basis of judging the relative merits of the models.
It is not that we believe that we can necessarily out-forecast the market in real time.
Indeed, our forecasting exercises are in the nature of ex post simulations, where inmany instances contemporaneous values of the right-hand-side variables are used
to predict future exchange rates. Rather, we construe the exercise as a means of protecting against data mining that might occur when relying solely on in-sample
inference.4
The exchange rate models considered in the exercise are summarized in Section 2.
Section 3 discusses the data, the estimation methods, and the criteria used to compare forecasting performance. The forecasting results are reported in Section 4. Section 5 concludes.

2. Theoretical models
The universe of empirical models that has been examined over the ﬂoating rate
period is enormous. Consequently any evaluation of these models must necessarily
be selective. Our criteria require that the models are (1) prominent in the economic
and policy literature, (2) readily implementable and replicable, and (3) not previously
evaluated in a systematic fashion. We use the random walk model as our benchmark
naive model, in line with previous work, but we also select the purchasing power parity and the basic Dornbusch (1976) and Frankel (1979) model as two comparator
speciﬁcations, as they still provide the fundamental intuition on how ﬂexible
4
There is an enormous literature on data mining. See Inoue and Kilian (2004) for some recent thoughtson the usefulness of out-of-sample versus in-sample tests.

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1153

exchange rates behave. The purchasing power parity condition examined in thisstudy is given by
st Zb0 Cp^t ;ð1Þwhere s is the log exchange rate, p is the log price level (CPI), and ‘‘ ˆ ’’ denotes theintercountry diﬀerence. Strictly speaking, Eq. (1) is the relative purchasing power
parity condition. The relative version is examined because price indices rather
than the actual price levels are considered.
The sticky-price monetary model can be expressed as follows:^ t Cb2 y^t Cb3 ^^ t Cut ;st Zb0 Cb1 m
it Cb4 pð2Þ

where m is log money, y is log real GDP, i and p are the interest and inﬂation rates, respectively, and ut is an error term. The characteristics of this model are well known, so
we will not devote time to discussing the theory behind the equation. We note, however,that the list of variables included in Eq. (2) encompasses those employed in the ﬂexible
price version of the monetary model, as well as the micro-based general equilibrium
models of Stockman (1980) and Lucas (1982). In addition, two observations are in order. First, the sticky-price model can be interpreted as an extension of Eq. (1) such thatthe price variables are replaced by macro variables that capture money demand andovershooting eﬀects. Second, we do not impose coeﬃcient restrictions in Eq. (2) because theory gives us little guidance regarding the exact values of all the parameters.
Next, we assess models that are in the BalassaeSamuelson vein, in that they accord a central role to productivity diﬀerentials to explaining movements in real, andhence also nominal, exchange rates. Real versions of the model can be traced to DeGregorio and Wolf (1994), while nominal versions include Clements and Frenkel(1980) and Chinn (1997). Such models drop the purchasing power parity assumption
for broad price indices, and allow the real exchange rate to depend upon the relative
price of nontradables, itself a function of productivity (z) diﬀerentials. A generic productivity diﬀerential exchange rate equation is^ t Cb2 y^t Cb3 ^st Zb0 Cb1 m
it Cb5 z^t Cut :ð3Þ

Although Eqs. (2) and (3) bear a superﬁcial resemblance, the two expressions embody quite diﬀerent economic and statistical implications. The central diﬀerence isthat Eq. (2) assumes PPP holds in the long run, while the productivity based model
makes no such presumption. In fact the nominal exchange rate can drift inﬁnitely far
away from PPP, although the path is determined in this model by productivity
diﬀerentials.
The fourth model is a composite model that incorporates a number of familiar
relationships. A typical speciﬁcation is:^ t Cb6 r^t Cb7 g^debtt Cb8 tott Cb9 nfat Cut ;st Zb0 Cp^t Cb5 uð4Þwhere u is the relative price of nontradables, r the real interest rate, gdebt the government debt to GDP ratio, tot the log terms of trade, and nfa is the net foreign

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Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

asset. Note that we impose a unitary coeﬃcient on the intercountry log price level p^,so that Eq. (4) could be re-expressed as determining the real exchange rate.
Although this particular speciﬁcation closely resembles the behavioral equilibrium
exchange rate (BEER) model of Clark and MacDonald (1999), it also shares attributes with the NATREX model of Stein (1999) and the real equilibrium exchange rate
model of Edwards (1989), as well as a number of other approaches. Consequently,
we will henceforth refer to this speciﬁcation as the ‘‘composite’’ model. Again, relative to Eq. (1), the composite model incorporates the BalassaeSamuelson eﬀect (viau), the overshooting eﬀect (r), and the portfolio balance eﬀect (gdebt, nfa).5
Models based upon this framework have been the predominant approach to determining the rate at which currencies will gravitate to over some intermediate horizon, especially in the context of policy issues. For instance, the behavioral
equilibrium exchange rate approach is the model that is most often used to determine
the long-term value of the euro.6
The ﬁnal speciﬁcation assessed is not a model per se; rather it is an arbitrage relationship e uncovered interest rate parity:
stCk Zst Ci^i;kð5Þwhere it,k is the interest rate of maturity k. Similar to the relative purchasing power
parity (1), this relation need not be estimated in order to generate predictions.
The interest rate parity is included in the forecast comparison exercise mainly because it has recently gathered empirical support at long horizons (Alexius, 2001;
Chinn and Meredith, 2004), in contrast to the disappointing results at the shorter horizons. MacDonald and Nagayasu (2000) have also demonstrated that long-run interest rates appear to predict exchange rate levels. On the basis of these ﬁndings, we
anticipate that this speciﬁcation will perform better at the longer horizons than atshorter horizons.7
3. Data, estimation and forecasting comparison
3.1. Data
The analysis uses quarterly data for the United States, Canada, UK, Japan, Germany, and Switzerland over the 1973q2 to 2000q4 period. The exchange rate, money,
price and income variables are drawn primarily from the IMF’s International5
On this latter channel, Cavallo and Ghironi (2002) provide a role for net foreign assets in the determination of exchange rates in the sticky-price optimizing framework of Obstfeld and Rogoﬀ (1995).
6
We do not examine a closely related approach, the internaleexternal balance approach of the IMF (seeFaruqee et al., 1999). The IMF approach requires extensive judgments regarding the trend level of output,
and the impact of demographic variables upon various macroeconomic aggregates. We did not believe it
would be possible to subject this methodology to the same out-of-sample forecasting exercise applied tothe others.
7
Despite this ﬁnding, there is little evidence that long-term interest rate diﬀerentials e or equivalently
long-dated forward rates e have been used for forecasting at the horizons we are investigating. One exception from the non-academic literature is Rosenberg (2001).

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1155

Financial Statistics. The productivity data were obtained from the Bank for International Settlements, while the interest rates used to conduct the interest rate parity
forecasts are essentially the same as those used in Chinn and Meredith (2004). See
the Appendix 1 for a more detailed description.
Two out-of-sample periods are used to assess model performance: 1987q2e
2000q4 and 1983q1e2000q4. The former period conforms to the post-Louvre Accord period, while the latter spans the period after the end of monetary targetingin the US. The shorter out-of-sample period (1987e2000) spans a period of relative
dollar stability (and appreciation in the case of the mark). The longer out-of-sample
period subjects the models to a more rigorous test, in that the prediction takes placeover a large dollar appreciation and subsequent depreciation (against the mark) anda large dollar depreciation (from 250 to 150 yen per dollar). In other words, this longer span encompasses more than one ‘‘dollar cycle.’’ The use of this long out-of-sample forecasting period has the added advantage that it ensures that there are many
forecast observations to conduct inference upon.
3.2. Estimation and forecasting
We adopt the convention in the empirical exchange rate modeling literature of implementing ‘‘rolling regressions’’ established by Meese and Rogoﬀ. That is, estimates
are applied over a given data sample, out-of-sample forecasts produced, then thesample is moved up, or ‘‘rolled’’ forward one observation before the procedure is repeated. This process continues until all the out-of-sample observations are exhausted. While the rolling regressions do not incorporate possible eﬃciency gains
as the sample moves forward through time, the procedure has the potential beneﬁtof alleviating parameter instability eﬀects over time e which is a commonly conceived phenomenon in exchange rate modeling.
Two speciﬁcations of these theoretical models were estimated: (1) an error correction speciﬁcation, and (2) a ﬁrst-diﬀerence speciﬁcation. These two speciﬁcations entail diﬀerent implications for interactions between exchange rates and theirdeterminants. It is well known that both the exchange rate and its economic determinants are I(1). The error correction speciﬁcation explicitly allows for the longrun interaction eﬀect of these variables (as captured by the error correction term)in generating forecast. On the other hand, the ﬁrst diﬀerences model emphasizes
the eﬀects of changes in the macro variables on exchange rates. If the variables
are cointegrated, then the former speciﬁcation is more eﬃcient than the latter one
and is expected to forecast better in long horizons. If the variables are not cointegrated, the error correction speciﬁcation can lead to spurious results. Because it is
not easy to determine unambiguously whether these variables are cointegrated ornot, we consider both speciﬁcations.
Since implementation of the error correction speciﬁcation is relatively involved,
we will address the ﬁrst-diﬀerence speciﬁcation to begin with. Consider the general
expression for the relationship between the exchange rate and fundamentals:
st ZXt GC3t ;

ð6Þ

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Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

where Xt is a vector of fundamental variables under consideration. The ﬁrst-diﬀerence speciﬁcation involves the following regression:
Dst ZDXt GCut :ð7Þ

These estimates are then used to generate one- and multi-quarter ahead forecasts.8
Since these exchange rate models imply joint determination of all variables in theequations, it makes sense to apply instrumental variables. However, previous experience indicates that the gains in consistency are far outweighed by the loss in eﬃciency,
in terms of prediction (Chinn and Meese, 1995). Hence, we rely solely on OLS.
The error correction estimation involves a two-step procedure. In the ﬁrst step,
the long-run cointegrating relation implied by Eq. (6) is identiﬁed using the Johansen~ is incorporated into the error corprocedure. The estimated cointegrating vector (G)rection term, and the resulting equation


~ Cut
st  stk Zd0 Cd1 stk  Xtk G
ð8Þ
is estimated via OLS. Eq. (8) can be thought of as an error correction model strippedof short-run dynamics. A similar approach was used in Mark (1995) and Chinn and
Meese (1995), except for the fact that in those two cases, the cointegrating vector was
imposed a priori. The use of this speciﬁcation is motivated by the diﬃculty in estimating the short-run dynamics in exchange rate equations.9
One key diﬀerence between our implementation of the error correction speciﬁcation and that undertaken in some other studies involves the treatment of the cointegrating vector. In some other prominent studies (MacDonald and Taylor, 1993), thecointegrating relationship is estimated over the entire sample, and then out-of-sample forecasting undertaken, where the short-run dynamics are treated as time varying
but the long-run relationship is not. While there are good reasons for adopting thisapproach e in particular one wants to use as much information as possible to obtain
estimates of the cointegrating relationships e the asymmetry in estimation approachis troublesome and makes it diﬃcult to distinguish quasi ex ante forecasts from true
ex ante forecasts. Consequently, our estimates of the long-run cointegrating relationship vary as the data window moves.10
It is also useful to stress the diﬀerence between the error correction speciﬁcation
forecasts and the ﬁrst-diﬀerence speciﬁcation forecasts. In the latter, ex post valuesof the right-hand-side variables are used to generate the predicted exchange rate
8
Only contemporaneous changes are involved in Eq. (8). While this is a somewhat restrictive assumption, it is not clear that allowing more lags would result in improved prediction. Moreover, implementation of a speciﬁcation procedure based upon some lag-selection criterion would be much too cumbersome
to implement in this context.
9
We opted to exclude short-run dynamics in Eq. (8) because a) the use of Eq. (8) yields true ex ante
forecasts and makes our exercise directly comparable with, for example, Mark (1995), Chinn and Meese(1995) and Groen (2000), and b) the inclusion of short-run dynamics creates additional demands on thegeneration of the right-hand-side variables and the stability of the short-run dynamics that complicate
the forecast comparison exercise beyond a manageable level.
10
Restrictions on the b-parameters in Eqs. (2), (3) and (4) are not imposed because in many cases we do
not have strong priors on the exact values of the coeﬃcients.

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1157

change. In the former, contemporaneous values of the right-hand-side variables are
not necessary, and the error correction predictions are true ex ante forecasts. Hence,
we are aﬀording the ﬁrst-diﬀerence speciﬁcations a tremendous informational advantage in forecasting.
3.3. Forecast comparison
To evaluate the forecasting accuracy of the diﬀerent structural models, the ratio
between the mean squared error (MSE) of the structural models and a driftless random walk is used. A value smaller (larger) than one indicates a better performance ofthe structural model (random walk). Inferences are based on a formal test for thenull hypothesis of no diﬀerence in the accuracy (i.e. in the MSE) of the two competing forecasts e structural model versus driftless random walk. In particular, we use
the DieboldeMariano statistic (Diebold and Mariano, 1995) which is deﬁned as theratio between the sample mean loss diﬀerential and an estimate of its standard error;
this ratio is asymptotically distributed as a standard normal.11 The loss diﬀerential isdeﬁned as the diﬀerence between the squared forecast error of the structural models
and that of the random walk. A consistent estimate of the standard deviation can beconstructed from a weighted sum of the available sample autocovariances of the loss
diﬀerential vector. Following Andrews (1991), a quadratic spectral kernel is employed, together with a data-dependent bandwidth selection procedure.12
We also examine the predictive power of the various models along diﬀerent dimensions. One might be tempted to conclude that we are merely changing thewell-established ‘‘rules of the game’’ by doing so. However, there are very good reasons to use other evaluation criteria. First, there is the intuitively appealing rationalethat minimizing the mean squared error (or relatedly mean absolute error) may not
be important from an economic standpoint. A less pedestrian motivation is that the
typical mean squared error criterion may miss out on important aspects of predictions, especially at long horizons. Christoﬀersen and Diebold (1998) point out thatthe standard mean squared error criterion indicates no improvement of predictions
that take into account cointegrating relationships vis à vis univariate predictions. But
surely, any reasonable criteria would put some weight on the tendency for predictions from cointegrated systems to ‘‘hang together.’’Hence, our ﬁrst alternative evaluation metric for the relative forecast performanceof the structural models is the direction of change statistic, which is computed as thenumber of correct predictions of the direction of change over the total number ofpredictions. A value above (below) 50% indicates a better (worse) forecasting
11
In using the DieboldeMariano test, we are relying upon asymptotic results, which may or may not beappropriate for our sample. However, generating ﬁnite sample critical values for the large number of cases
we deal with would be computationally infeasible. More importantly, the most likely outcome of such an
exercise would be to make detection of statistically signiﬁcant outperformance even more rare, and leaving
our basic conclusion intact.
12
We also experienced with the Bartlett kernel and the deterministic bandwidth selection method. The
results from these methods are qualitatively very similar. Appendix 2 contains a more detailed discussionof the forecast comparison tests.

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Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

performance than a naive model that predicts the exchange rate has an equal chance
to go up or down. Again, Diebold and Mariano (1995) provide a test statistic for thenull of no forecasting performance of the structural model. The statistic follows a binomial distribution, and its studentized version is asymptotically distributed as a standard normal. Not only does the direction of change statistic constitute an alternative
metric, Leitch and Tanner (1991), for instance, argue that a direction of change criterion may be more relevant for proﬁtability and economic concerns, and hencea more appropriate metric than others based on purely statistical motivations. The
criterion is also related to tests for market timing ability (Cumby and Modest, 1987).
The third metric we used to evaluate forecast performance is the consistency criterion proposed in Cheung and Chinn (1998). This metric focuses on the time-series
properties of the forecast. The forecast of a given spot exchange rate is labeled asconsistent if (1) the two series have the same order of integration, (2) they are cointegrated, and (3) the cointegration vector satisﬁes the unitary elasticity of expectations condition. Loosely speaking, a forecast is consistent if it moves in tandemwith the spot exchange rate in the long run. While the two previous criteria focus
on the precision of the forecast, the consistency requirement is concerned with thelong-run relative variation between forecasts and actual realizations. One may argue
that the criterion is less demanding than the MSE and direction of change metrics. A
forecast that satisﬁes the consistency criterion can (1) have an MSE larger than thatof the random walk model, (2) have a direction of change statistic less than 1/2, or(3) generate forecast errors that are serially correlated. However, given the problems
related to modeling, estimation, and data quality, the consistency criterion can bea more ﬂexible way to evaluate a forecast. Cheung and Chinn (1998) provide
a more detailed discussion on the consistency criterion and its implementation.
It is not obvious which one of the three evaluation criteria is better as they eachhave a diﬀerent focus. The MSE is a standard evaluation criterion, the direction ofchange metric emphasizes the ability to predict directional changes, and the consistency test is concerned about the long-run interactions between forecasts and theirrealizations. Instead of arguing one criterion is better than the other, we consider
the use of these criteria as complementary and providing a multifaceted picture of
the forecast performance of these structural models. Of course, depending on the
purpose of a speciﬁc exercise, one may favor one metric over the other.

4. Comparing the forecast performance
4.1. The MSE criterion
The comparison of forecasting performance based on MSE ratios is summarizedin Table 1. The table contains MSE ratios and the p-values from ﬁve dollar-based currency pairs, ﬁve model speciﬁcations, the error correction and ﬁrst-diﬀerence speciﬁcations, three forecasting horizons, and two forecasting samples. Each cell in thetable has two entries. The ﬁrst one is the MSE ratio (the MSEs of a structural modelto the random walk speciﬁcation). The entry underneath the MSE ratio is the p-value

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Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175
Table 1The MSE ratios from the dollar-based exchange rates
Speciﬁcation Horizon Sample 1: 1987q2e2000q4

Panel A: BP/$
ECM
1
4
20
FD

PPP

S-P

IRP

PROD COMP PPP

S-P

IRP

PROD COMP

4.165
0.003
1.750
0.199
0.782
0.536

1.047
0.409
1.127
0.503
1.809
0.014

1.008
0.883
1.092
0.620
1.342
0.240

0.995
0.897
1.017
0.802
1.095
0.411

1.085
0.208
1.099
0.253
1.340
0.168

1.050
0.310
1.142
0.171
1.457
0.071

1.046
0.318
1.123
0.310
0.841
0.518

1.042
0.303
1.085
0.237
1.545
0.092

1.049
0.448
1.127
0.225
2.179
0.057

1.006
0.940
1.124
0.524
2.531
0.021

1.191
0.217
1.881
0.001
6.953
0.000

1.079
0.337
1.455
0.176
5.557
0.019

1.023
0.901
1.448
0.351
6.015
0.001

1.148
0.062
1.182
0.157
1.090
0.308

1.278
0.016
1.603
0.118
1.760
0.002

1.041
0.552
1.017
0.929
1.097
0.318

1.337
0.004
1.754
0.018
1.623
0.000

1.115
0.138
1.160
0.341
0.504
0.182

0.614
0.109
0.899
0.798
1.924
0.006

1.171
0.047
1.269
0.192
2.004
0.143

0.666
0.151
1.143
0.704
2.289
0.204

1.041
0.574
1.080
0.282
1.131
0.141

0.995
0.955
1.116
0.642
2.137
0.216

0.997
0.961
0.949
0.626
1.260
0.039

0.911
0.206
0.898
0.558
0.633
0.202

1.324
0.106
1.607
0.030
1.927
0.114

0.555
0.001
0.844
0.571
2.522
0.140

1.196
0.084
1.281
0.009
1.964
0.121

0.694
0.020
1.151
0.612
3.975
0.003

1.024
0.515
1.184
0.367

.
.
.
.

1.052
0.581
1.136
0.149

.
.
.
.

1

1.041
0.434
1.120
0.315
1.891
0.177

4
20
Panel B: CAN$/$
ECM
1
4
20
FD

32.205
0.008
6.504
0.016
1.569
0.000

1

20

4
20
FD

6.357
0.006
2.301
0.016
0.649
0.363

1

20

4

1.090
0.048
1.172
0.452
0.865
0.760

1.059
0.464
1.080
0.444
1.047
0.637

1.030
0.295
1.136
0.069
0.596
0.167

1.268
0.052
1.402
0.024
1.814
0.175

4

Panel D: SF/$
ECM
1

1.054
0.127
1.102
0.181
0.939
0.574
1.100
0.179
1.137
0.461
0.515
0.193

4

Panel C: DM/$
ECM
1

Sample 2: 1983q1e2000q4

7.595
0.001
2.537
0.014

1.074
0.187
1.269
0.015

1.051
0.138
1.183
0.059

5.678
0.031
1.612
0.224
0.632
0.156

1.086
0.135
1.250
0.149
3.223
0.195
31.982
0.001
6.947
0.004
1.171
0.093

1.056
0.279
1.116
0.334
1.062
0.727

1.092
0.022
1.170
0.359
0.813
0.607

1.101
0.257
1.196
0.347
1.892
0.182
11.173
0.005
2.675
0.007
0.411
0.248

1.105
0.416
1.104
0.599
1.771
0.212

1.029
0.364
1.063
0.485
0.895
0.656

1.123
0.017
1.077
0.452
1.723
0.246
8.694
0.000
2.106
0.003

0.995
0.906
1.002
0.982

1.050
0.141
1.122
0.248

(continued on next page)1160

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

Table 1 (continued)
Speciﬁcation Horizon Sample 1: 1987q2e2000q4
PPP
20
FD

1.106
0.189
1.362
0.004
2.477
0.039

4
20

4
20
FD

1
4
20

IRP

PROD COMP PPP

1.185 1.621 1.489 0.969
0.514 0.069 0.000 0.934

1Panel E: Yen/$
ECM
1

S-P

15.713
0.003
4.973
0.022
1.797
0.149

1.067
0.312
1.189
0.279
0.951
0.647
1.085
0.321
1.004
0.978
1.081
0.912

1.049
0.251
1.174
0.247
0.603
0.227

Sample 2: 1983q1e2000q4

.
.

1.090
0.351
1.468
0.001
2.657
0.049

.
.
.
.
.
.

1.073
0.125
1.239
0.151
1.011
0.851

.
.
.
.
.
.

1.048
0.480
1.023
0.881
0.973
0.963

.
.
.
.
.
.

S-P

IRP

PROD COMP

0.634 1.367 1.489 1.377
0.431 0.046 0.000 0.011
1.089
0.237
1.232
0.153
1.540
0.521
10.510
0.000
2.582
0.015
0.832
0.585

1.008
0.920
1.015
0.874
1.175
0.049
1.165
0.179
0.994
0.969
0.924
0.844

1.032
0.361
1.048
0.658
0.566
0.174

.
.

1.067
0.545
1.332
0.050
1.870
0.394

.
.
.
.
.
.

1.064
0.281
1.234
0.004
1.235
0.076

.
.
.
.
.
.

1.141
0.220
1.012
0.929
1.023
0.957

.
.
.
.
.
.

Note: The results are based on dollar-based exchange rates and their forecasts. Each cell in the table has
two entries. The ﬁrst one is the MSE ratio (the MSEs of a structural model to the random walk speciﬁcation). The entry underneath the MSE ratio is the p-value of the hypothesis that the MSEs of the structural and random walk models are the same (based on Diebold and Mariano, 1995, described in Appendix2). The notations used in the table are ECM: error correction speciﬁcation; FD: ﬁrst-diﬀerence speciﬁcation; PPP: purchasing power parity model; S-P: sticky-price model; IRP: interest rate parity model;
PROD: productivity diﬀerential model; and COMP: composite model. The forecasting horizons (in quarters) are listed under the heading ‘‘Horizon.’’ The results for the post-Louvre Accord forecasting period
are given under the label ‘‘Sample 1’’ and those for the post-1983 forecasting period are given under
the label ‘‘Sample 2.’’ A ‘‘.’’ indicates the statistics are not generated due to unavailability of data.

of the DieboldeMariano statistic testing the null hypothesis that the diﬀerence of theMSEs of the structural and random walk models is zero (i.e. there is no diﬀerence inthe forecast accuracy of the structural and the random walk model). Because of thelack of data, the composite model is not estimated for the dollareSwiss franc and dollareyen exchange rates. Altogether, there are 216 MSE ratios, which spread evenly
across the two forecasting samples. Of these 216 ratios, 138 are computed from theerror correction speciﬁcations and 78 from the ﬁrst-diﬀerence ones.
Note that in the tables, only ‘‘error correction speciﬁcation’’ entries are reported
for the purchasing power parity and interest rate parity models. In fact, the twomodels are not estimated; rather the predicted spot rate is calculated using the parity
conditions. To the extent that the deviation from a parity condition can be considered the error correction term, we believe this categorization is most appropriate.

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1161

Overall, the MSE results are not favorable to the structural models. Of the 216
MSE ratios, 151 are not signiﬁcant (at the 10% signiﬁcance level) and 65 are significant. That is, for the majority cases one cannot diﬀerentiate the forecasting performance between a structural model and a random walk model. For the 65 signiﬁcantcases, there are 63 cases in which the random walk model is signiﬁcantly better thanthe competing structural models and only two cases in which the opposite is true.
The signiﬁcant cases are quite evenly distributed across the two forecasting periods.
As 10% is the size of the test and two cases constitute less than 10% of the total of
216 cases, the empirical evidence can hardly be interpreted as supportive of the superior forecasting performance of the structural models.
Inspection of the MSE ratios does not reveal many consistent patterns in terms ofoutperformance. It appears that the productivity model does not do particularly
badly for the dollaremark rate at the 1- and 4-quarter horizons. The MSE ratiosof the purchasing power parity and interest rate parity models are less than unity(even though not signiﬁcant) only at the 20-quarter horizon e a ﬁnding consistent
with the perception that these parity conditions work better at long rather than atshort horizons. As the yen-based results for the MSE ratios e as well as the othertwo metrics e display the same pattern, we do not report them. They can be foundin the working paper version of this article (Cheung et al., 2003).
Consistent with the existing literature, our results are supportive of the assertion
that it is very diﬃcult to ﬁnd forecasts from a structural model that can consistently
beat the random walk model using the MSE criterion. The current exercise further
strengthens the assertion as it covers both dollar- and yen-based exchange rates,
two diﬀerent forecasting periods, and some structural models that have not been extensively studied before.

4.2. The direction of change criterion
Table 2 reports the proportion of forecasts that correctly predict the direction of
the dollar exchange rate movement and, underneath these sample proportions, the pvalues for the hypothesis that the reported proportion is signiﬁcantly diﬀerent from
1/2. When the proportion statistic is signiﬁcantly larger than 1/2, the forecast is said
to have the ability to predict the direction of change. On the other hand, if the statistic is signiﬁcantly less than 1/2, the forecast tends to give the wrong direction ofchange. For trading purposes, information regarding the signiﬁcance of incorrect
prediction can be used to derive a potentially proﬁtable trading rule by going again
the prediction generated by the model. Following this argument, one might consider
the cases in which the proportion of ‘‘correct’’ forecasts is larger than or less than 1/2
contain the same information. However, in evaluating the ability of the model to describe exchange rate behavior, we separate the two cases.
There is mixed evidence on the ability of the structural models to correctly predictthe direction of change. Among the 216 direction of change statistics, 50 (23) are signiﬁcantly larger (less) than 1/2 at the 10% level. The occurrence of the signiﬁcant outperformance cases is higher (23%) than the one implied by the 10% level of the test.

1162

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

Table 2
Direction of change statistics from the dollar-based exchange rates
Speciﬁcation Horizon Sample 1: 1987q2e2000q4

Panel A: BP/$
ECM
1
4
20
FD

PPP

S-P

IRP

PROD COMP PPP

S-P

IRP

PROD COMP

0.527
0.686
0.596
0.166
0.361
0.096

0.546
0.500
0.577
0.267
0.389
0.182

0.464
0.593
0.500
1.000
0.536
0.593

0.564
0.345
0.519
0.782
0.472
0.739

0.527
0.686
0.481
0.782
0.361
0.096

0.569
0.239
0.522
0.718
0.509
0.891

0.411
0.128
0.425
0.198
0.589
0.128

0.528
0.637
0.464
0.547
0.491
0.891

0.528
0.637
0.507
0.904
0.359
0.039

0.473
0.686
0.577
0.267
0.556
0.505

0.418
0.225
0.365
0.052
0.500
1.000

0.500
1.000
0.667
0.006
0.453
0.492

0.556
0.346
0.536
0.547
0.491
0.891

0.400
0.138
0.423
0.267
0.472
0.739

0.382
0.080
0.346
0.027
0.083
0.000

0.500
1.000
0.594
0.118
0.509
0.891

0.458
0.480
0.319
0.003
0.151
0.000

0.473
0.686
0.519
0.782
0.889
0.000

0.618
0.080
0.673
0.013
0.583
0.317

0.444
0.346
0.493
0.904
0.604
0.131

0.611
0.059
0.623
0.041
0.509
0.891

0.455
0.500
0.462
0.579
0.333
0.046

0.491
0.893
0.462
0.579
0.333
0.046

0.500
1.000
0.449
0.399
0.434
0.336

0.486
0.814
0.507
0.904
0.509
0.891

0.473
0.686
0.462
0.579
0.639
0.096

0.800
0.000
0.673
0.013
0.667
0.046

0.444
0.346
0.449
0.399
0.415
0.216

0.750
0.000
0.609
0.071
0.472
0.680

1

0.455
0.500
0.481
0.782
0.639
0.096

4
20

Panel B: CAN$/$
ECM
1
4
20
FD

0.527
0.686
0.769
0.000
0.944
0.000

1

20

4
20
FD

1
4
20

Panel D: SF/$
ECM
1

0.473
0.686
0.442
0.405
0.500
1.000

0.429
0.285
0.339
0.016
0.732
0.001

0.509
0.893
0.539
0.579
0.889
0.000

4

Panel C: DM/$
ECM
1

Sample 2: 1983q1e2000q4

0.545
0.500
0.654
0.027
0.778
0.001

0.636
0.043
0.635
0.052
0.583
0.317
0.455
0.500
0.365
0.052
0.611
0.182

0.357
0.033
0.429
0.285
0.696
0.003

0.600 0.400 0.339 0.618
0.138 0.138 0.016 0.080

.
.

0.583
0.157
0.652
0.011
0.623
0.074

0.472
0.637
0.507
0.904
0.415
0.216

0.569
0.239
0.783
0.000
0.962
0.000

0.514
0.814
0.536
0.547
0.472
0.680

0.425
0.198
0.370
0.026
0.767
0.000

0.542
0.480
0.478
0.718
0.585
0.216

0.514
0.814
0.652
0.011
0.717
0.002

0.486
0.814
0.449
0.399
0.283
0.002
0.444
0.346
0.493
0.904
0.509
0.891

0.411
0.128
0.425
0.198
0.589
0.128

0.611 0.542 0.384 0.625
0.059 0.480 0.047 0.034

.
.

1163

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175
Table 2 (continued)
Speciﬁcation Horizon Sample 1: 1987q2e2000q4

4
20
FD

PPP

S-P

IRP

PROD COMP PPP

S-P

IRP

PROD COMP

0.558
0.405
0.750
0.003

0.404
0.166
0.444
0.505

0.411
0.182
0.455
0.670

0.539
0.579
0.583
0.317

.
.
.
.

0.580
0.185
0.528
0.680

0.425
0.198
0.455
0.670

0.580
0.185
0.434
0.336

.
.
.
.

0.400
0.138
0.308
0.006
0.611
0.182

.
.
.
.
.
.

0.458
0.480
0.362
0.022
0.698
0.004

.
.
.
.
.
.

0.546
0.500
0.519
0.782
0.556
0.505

.
.
.
.
.
.

0.514
0.814
0.406
0.118
0.340
0.020

.
.
.
.
.
.

0.564
0.345
0.596
0.166
0.583
0.317

.
.
.
.
.
.

0.542
0.480
0.652
0.012
0.736
0.001

.
.
.
.
.
.

1

0.436
0.345
0.346
0.027
0.611
0.182

4
20

Panel E: Yen/$
ECM
1
4
20
FD

1
4
20

Sample 2: 1983q1e2000q4

0.527
0.686
0.673
0.013
0.611
0.182

0.527
0.686
0.577
0.267
0.556
0.505
0.582
0.225
0.654
0.027
0.611
0.182

0.375
0.061
0.482
0.789
0.696
0.003

0.638
0.022
0.811
0.000

0.444
0.346
0.435
0.279
0.717
0.002

0.597
0.099
0.681
0.003
0.811
0.000

0.597
0.099
0.623
0.041
0.415
0.216
0.583
0.157
0.652
0.012
0.755
0.000

0.425
0.198
0.548
0.413
0.703
0.001

Note: Table 3 reports the proportion of forecasts that correctly predict the direction of the dollar exchange
rate movement. Underneath each direction of change statistic, the p-values for the hypothesis that the reported proportion is signiﬁcantly diﬀerent from 1/2 is listed. When the statistic is signiﬁcantly larger than
1/2, the forecast is said to have the ability to predict the direction of change. If the statistic is signiﬁcantly
less than 1/2, the forecast tends to give the wrong direction of change. The notations used in the table are
ECM: error correction speciﬁcation; FD: ﬁrst-diﬀerence speciﬁcation; PPP: purchasing power parity model; S-P: sticky-price model; IRP: interest rate parity model; PROD: productivity diﬀerential model; andCOMP: composite model. The forecasting horizons (in quarters) are listed under the heading ‘‘Horizon.’’The results for the post-Louvre Accord forecasting period are given under the label ‘‘Sample 1’’ and thosefor the post-1983 forecasting period are given under the label ‘‘Sample 2.’’ A ‘‘.’’ indicates the statistics are
not generated due to unavailability of data.

The results indicate that the structural model forecasts can correctly predict the direction of the change, while the proportion of cases where a random walk outperforms thecompeting models is only about what one would expect if they occurred randomly.
Let us take a closer look at the incidences in which the forecasts are in the right
direction. Approximately 58% of the 50 cases are associated with the error correction model and the remainder with the ﬁrst diﬀerence speciﬁcation. Thus, the error
correction speciﬁcation e which incorporates the empirical long-run relationship eprovides a slightly better speciﬁcation for the models under consideration. The forecasting period does not have a major impact on forecasting performance, sinceexactly half of the successful cases are in each forecasting period.

1164

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

Among the ﬁve models under consideration, the purchasing power parity speciﬁcation has the highest number (18) of forecasts that give the correct direction ofchange prediction, followed by the sticky-price, composite, and productivity models(10, 9, and 8, respectively), and the interest rate parity model (5). Thus, at least on
this count, the newer exchange rate models do not edge out the ‘‘old fashioned’’ purchasing power parity doctrine and the sticky-price model. Because there are diﬀering
numbers of forecasts due to data limitations and speciﬁcations, the proportions do
not exactly match up with the numbers. Proportionately, the purchasing power model
does the best.
Interestingly, the success of direction of change prediction appears to be currency
speciﬁc. The dollareyen exchange rate yields 13 out of 50 forecasts that give the correct direction of change prediction. In contrast, the dollarepound has only four out
of 50 forecasts that produce the correct direction of change prediction.
The cases of correct direction prediction appear to cluster at the long forecast horizon. The 20-quarter horizon accounts for 22 of the 50 cases while the 4- and 1quarter horizons have 18 and 10 direction of change statistics, respectively, thatare signiﬁcantly larger than 1/2. Since there have not been many studies utilizing
the direction of change statistic in similar contexts, it is diﬃcult to make comparisons. Chinn and Meese (1995) apply the direction of change statistic to 3-year horizons for three conventional models, and ﬁnd that performance is largely currency
speciﬁc: the no change prediction is outperformed in the case of the dollareyen exchange rate, while all models are outperformed in the case of the dollarepound rate.
In contrast, in our study at the 20-quarter horizon, the positive results appear to be
fairly evenly distributed across the currencies, with the exception of the dollare
pound rate.13 Mirroring the MSE results, it is interesting to note that the directionof change statistic works for the purchasing power parity at the 4- and 20-quarter
horizons and for the interest rate parity model only at the 20-quarter horizon.
This pattern is entirely consistent with the ﬁndings that the two parity conditions
hold better at long horizons.14

4.3. The consistency criterion
The consistency criterion only requires the forecast and actual realization comove
one-to-one in the long run. In assessing the consistency, we ﬁrst test if the forecast
and the realization are cointegrated.15 If they are cointegrated, then we test if the
13
Using Markov switching models, Engel (1994) obtains some success along the direction of change dimension at horizons of up to 1 year. However, his results are not statistically signiﬁcant.
14
Flood and Taylor (1997) noted the tendency for PPP to hold better at longer horizons. Mark and Moh(2001) document the gradual currency appreciation in response to a short-term interest diﬀerential, contrary to the predictions of uncovered interest parity.
15
The Johansen method is used to test the null hypothesis of no cointegration. The maximum eigenvalue
statistics are reported in the manuscript. Results based on the trace statistics are essentially the same. Before implementing the cointegration test, both the forecast and exchange rate series were checked for theI(1) property. For brevity, the I(1) test results and the trace statistics are not reported.

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1165

cointegrating vector satisﬁes the (1, 1) requirement. The cointegration results are reported in Table 3, while the test results for the (1, 1) restriction are reported in Table 4.
In Table 3, 67 of 216 cases reject the null hypothesis of no cointegration at the 10%
signiﬁcance level. Thus, 67 forecast series (31% of the total number) are cointegrated
with the corresponding spot exchange rates. The error correction speciﬁcation accounts for 39 of the 67 cointegrated cases and the ﬁrst-diﬀerence speciﬁcation accounts
for the remaining 28 cases. There is some evidence that the error correction speciﬁcation gives better forecasting performance than the ﬁrst-diﬀerence speciﬁcation. These
67 cointegrated cases are slightly more concentrated in the longer of the two forecasting periods e 30 for the post-Louvre Accord period and 37 for the post-1983 period.
Interestingly, the sticky-price model garners the largest number of cointegrated cases.
There are 60 forecast series generated under the sticky-price model. Twenty-six of these
60 series (i.e. 43%) are cointegrated with the corresponding spot rates. The composite
model has the second highest frequency of cointegrated forecast series e 39% of 36 series. Thirty-seven percent of the productivity diﬀerential model forecast series, 33% of
the purchasing power parity model, and none of the interest rate parity model are cointegrated with the spot rates. Apparently, we do not ﬁnd evidence that the recently developed exchange rate models outperform the ‘‘old’’ vintage sticky-price model.
The dollarepound and dollareCanadian dollar, each have between 19 and 17
forecast series that are cointegrated with their respective spot rates. The dollare
mark pair, which yields relatively good forecasts according to the direction of change
metric, has only 12 cointegrated forecast series. Evidently, the forecasting performance is not just currency speciﬁc; it also depends on the evaluation criterion.
The distribution of the cointegrated cases across forecasting horizons is puzzling.
The frequency of occurrence is inversely proportional to the forecasting horizons.
There are 35 of 67 one-quarter ahead forecast series that are cointegrated with the
spot rates. However, there are only 20 of the 4-quarter ahead and 12 of the 20-quarter ahead forecast series that are cointegrated with the spot rates. One possible explanation for this result is that there are fewer observations in the 20-quarter ahead
forecast series and this aﬀects the power of the cointegration test.
The results of testing for the long-run unitary elasticity of expectations at the 10% signiﬁcance level are reported in Table 4. The condition of long-run unitary elasticity of expectations e that is the (1,1) restriction on the cointegrating vector e is rejected by thedata quite frequently: 48 of the 67 cointegration cases. That is 28% of the cointegrated
cases display long-run unitary elasticity of expectations. Taking both the cointegration
and restriction test results together, 9% of the 216 cases of the dollar-based exchange
rate forecast series meet the consistency criterion. A slightly higher proportion(12%) meet the consistency criterion in the case of the yen-based exchange rates (results
not reported), but the pattern is essentially the same as for the dollar-based exchange
rates.
4.4. Discussion
Several aspects of the foregoing analysis merit discussion. To begin with, even atlong horizons, the performance of the structural models is less than impressive along

Table 3
Cointegration between dollar-based exchange rates and their forecasts
Speciﬁcation Horizon Sample 1: 1987q2e2000q4
PPP
Panel A: BP/$
ECM
1
4
20
FD

FD

1
4
20

Panel C: DM/$
ECM
1
4
20
FD

5.59
7.15
5.99

1
4
20

13.03*
2.21
3.44

11.64* 1.29 4.37
10.27* 2.53 4.55
15.02* 3.98 19.82*

10.35*
5.39
9.67*

26.34*
3.19
10.03*

31.53*
3.87
9.59*

9.19
3.88
6.72

3.86
5.37
7.55

5.23
18.33*
9.20

4.02
3.16
8.62

8.29
15.29*
3.74

3.80
9.10
1.81

.
.
.

20.30*
6.71
7.51

.
.
.

1.84
3.22
2.19

.
.
.

9.79*
3.77
2.15

.
.
.

3.67
5.24
6.09

5.19
2.74
1.63

6.75
8.55
1.16

3.45
2.07
6.93

33.01*
10.96*
9.43

9.42
9.01
6.38

12.64*
84.86*
6.95

20.85*
6.71
13.00*

20.82*
4.27
5.42

1
4
20

Panel E: Yen/$
ECM
1
4
20
FD

2.17
4.75
11.28*

1
4
20

Panel D: SF/$
ECM
1
4
20
FD

25.63*
7.30
8.45

0.76
2.38
9.50

Sample 2: 1983q1e2000q4

IRP PROD COMP PPP

5.25
7.26 0.77 6.95
10.03* 8.56 1.47 9.66*
26.64* 15.84* 5.30 18.82*

1
4
20

Panel B: CAN$/US$
ECM
1
4
20

S-P

2.19
3.43
4.67
13.35*
5.53
1.76

6.94
4.13
2.93

S-P

IRP PROD COMP

3.41 17.09* 4.60 10.40*
6.75 12.98* 3.77 7.88
10.62* 3.16 5.03 4.25
34.00*
6.98
3.57

32.83*
18.94*
4.72

8.60
3.02
2.79

16.91*
3.45
2.24

14.31* 1.90 13.96*
6.37 1.53 9.58*
2.61 4.18 1.60

19.66*
13.52*
2.19

25.72*
6.99
1.45

9.89*
8.63
2.21

8.12
3.89
3.52

12.68* 2.84 27.29*
24.06* 1.81 6.67
3.56 2.37 2.94

21.03*
8.49
16.60*

36.32*
7.56
3.69

35.91*
10.82*
4.16

2.18
2.80
4.26

22.10* 3.23
10.71* 2.27
2.93 6.93

6.33
9.68*
2.96

.
.
.

23.55*
14.33*
2.27

10.38*
13.74*
2.59.
.
.

6.96 19.44* 6.45 12.73*
10.46* 10.71* 3.27 14.79*
6.76
2.90 3.48 5.63

.
.
.

8.43
7.78
3.07

2.27
5.76
6.80

4.58
5.58
1.37

15.47*
6.02
4.94

15.47*
5.74
3.96

.
.
.

Note: The Johansen maximum eigenvalue statistic for the null hypothesis that a dollar-based exchange rateand its forecast are not cointegrated. ‘‘*’’ indicates 10% level signiﬁcance. Tests for the null of one cointegrating vector were also conducted but in all cases the null was not rejected. The notations used in thetable are ECM: error correction speciﬁcation; FD: ﬁrst-diﬀerence speciﬁcation; PPP: purchasing power
parity model; S-P: sticky-price model; IRP: interest rate parity model; PROD: productivity diﬀerential
model; and COMP: composite model. The forecasting horizons (in quarters) are listed under the heading‘‘Horizon.’’ The results for the post-Louvre Accord forecasting period are given under the label ‘‘Sample
1’’ and those for the post-1983 forecasting period are given under the label ‘‘Sample 2.’’ A ‘‘.’’ indicates thestatistics are not generated due to unavailability of data.

1167

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175
Table 4
Results of the (1, 1) restriction rest: dollar-based exchange rates
Speciﬁcation Horizon Sample 1: 1987q2e2000q4
PPP

S-P

Sample 2: 1983q1e2000q4

IRP PROD COMP PPP

Panel A: BP/$
ECM
1
4
20
FD

10.29
0.00
36.66
0.00

1

0.40
0.53

0.98
0.32
0.36
0.55

5.38
0.02

0.12
0.73

0.55
0.46
1.02
0.31

S-P
3.38
0.07
2.59
0.11

IRP PROD COMP
0.00
1.00

0.35
0.56
0.09
0.76

15.97
0.00
0.04
0.83

0.79
0.38

0.36
0.55

4.46
0.03

7.75
0.01

2.87
0.09
5.36
0.02

13.90
0.00

5.47
0.02

8.82
0.00
6.31
0.01

8.35
0.00

4
20

23.20
0.00

Panel B: CAN$/$
ECM
1
4
20
FD

1

11.20
0.00
24.05
0.00
76.59
0.00

82.26
0.00

7.81
0.01

6.09
0.01

4.39
0.04

3.50
0.06

6.48
0.01
4.52
0.03

201.370.00

420
Panel C: DM/$
ECM
1
4
20
FD

1

3.20
0.07
558
0.00

6.61
0.01

27.81
0.00
10.17
0.00

3.03
0.08

4

25.21
0.00

0.47
0.49
7.39
0.01

20
Panel D: SF/$
ECM
1
4
20

.
.
.
.
.

10.07
0.00
2.40
0.12

10.96
0.00

.
.
.
.
.

(continued on next page)

1168

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

Table 4 (continued)
Speciﬁcation Horizon Sample 1: 1987q2e2000q4
PPP
FD

1
4

S-P
20.17
0.00
20.87
0.00

IRP PROD COMP PPP
20.82
0.00

20
Panel E: Yen/$
ECM
1
4
20
FD

1
4
20

6.76
0.01

Sample 2: 1983q1e2000q4

5.40
0.02

S-P

IRP PROD COMP

.
.
.
.
.

4.57
0.03
8.84
0.00

4.79
0.03
8.40
0.00

.
.
.
.
.

.
.
.
.
.

3.22
0.07
0.55
0.46

2.47
0.12
5.71
0.02

.
.
.
.
.

0.45
0.50

0.71
0.40

.
.
.
.
.

.
.
.
.
.

350
0.00

Note: The likelihood ratio test statistic for the restriction of (1, 1) on the cointegrating vector and its pvalue are reported. The test is only applied to the cointegration cases present in Table 3. The notations
used in the table are ECM: error correction speciﬁcation; FD: ﬁrst-diﬀerence speciﬁcation; PPP: purchasing power parity model; S-P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and COMP: composite model. The forecasting horizons (in quarters) are listed under theheading ‘‘Horizon.’’ The results for the post-Louvre Accord forecasting period are given under the label‘‘Sample 1’’ and those for the post-1983 forecasting period are given under the label ‘‘Sample 2.’’ A ‘‘.’’
indicates the statistics are not generated due to unavailability of data.

the MSE dimension. This result is consistent with those in other recent studies, although we have documented this ﬁnding for a wider set of models and speciﬁcations.
Groen (2000) restricted his attention to a ﬂexible price monetary model, while Faust
et al. (2003) examined a portfolio balance model as well; both remained within the
MSE evaluation framework.
Setting aside issues of statistical signiﬁcance, it is interesting that long horizon error
correction speciﬁcations are over-represented in the set of cases where a random walkis outperformed. Indeed, the purchasing power parity and interest rate parity
models at the 20-quarter horizon account for many of the MSE ratio entries thatare less than unity (13 of 23 error correction dollar-based entries, and 14 of 33 yenbased entries).
The fact that outperformance of the random walk benchmark occurs at the longhorizons is consistent with other recent work. As Engel and West (2005) have noted,
if the discount factor is near unity, and at least one of the driving variables
follows a near unit root process, the exchange rate may appear to be very close
to a random walk, and exhibit very little predictability at short horizons. But at longer horizons, this characterization may be less apt, especially if it is the case

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1169

that exchange rates are not weakly exogenous with respect to the cointegrating
vector.16
Expanding the set of criteria does yield some interesting surprises. In particular,
the direction of change statistics indicates more evidence that structural models
can outperform a random walk. However, the basic conclusion that no speciﬁc economic model is consistently more successful than the others remains intact. This, we
believe, is a new ﬁnding.17
Even if we cannot glean from this analysis a consistent ‘‘winner’’, it may still be ofinterest to note the best and worst performing combinations of model/speciﬁcation/
currency. Of the reported results, the interest rate parity model at the 20-quarter horizon for the dollareyen exchange rate (post-1982) performs best according to the
MSE criterion, with an MSE ratio of 0.57 ( p-value of 0.17). (The corresponding results for the Canadian dollareyen exchange rate are even better, with a ratio of 0.48
( p-value of 0.04); see Cheung et al., 2003, Table 2.)Note, however, that the superior performance of a particular model/speciﬁcation/
currency combination does not necessarily carry over from one out-of-sample period
to the other. That is the lowest dollar-based MSE ratio during the 1987q2e2000q4
period is for the Deutsche mark composite model in ﬁrst diﬀerences, while the corresponding entry for the 1983q1e2000q4 period is for the yen interest parity model.
Aside from the purchasing power parity speciﬁcation, the worst performances areassociated with ﬁrst-diﬀerence speciﬁcations; in this case the highest MSE ratio isfor the ﬁrst-diﬀerence speciﬁcation of the composite model at the 20-quarter horizon
for the poundedollar exchange rate over the post-Louvre period. However, the othercatastrophic failures in prediction performance are distributed across the various models estimated in ﬁrst diﬀerences, so (taking into account the fact that these predictions
utilize ex post realizations of the right-hand-side variables) the key determinant in thispattern of results appears to be the diﬃculty in estimating stable short-run dynamics.
That being said, we do not wish to overplay the stability of the long-run estimates
we obtain. In a companion study (Cheung et al., 2005), we do not ﬁnd a deﬁnite relationship between in-sample ﬁt and out-of-sample forecast performance. Moreover,the estimates exhibit wide variation over time. Even in cases where the structuralmodel does reasonably well, there is quite substantial time-variation in the estimateof the rate at which the exchange rate responds to disequilibria. A similar observation applies to the coeﬃcient estimates of the parameters of the cointegrating vector.
Thus, an interesting future research topic is to further investigate the eﬀect of imposing parameter restrictions and the interaction between parameter instability andforecast performance.
16
Engel and West (2005) use Granger causality tests to conduct their inference. Since they fail to ﬁnd
cointegration of the exchange rate with the monetary fundamentals, they do not conduct tests for weakexogeneity. However, other studies, spanning diﬀerent sample periods and models, have detected both cointegration; see for instance MacDonald and Marsh (1999) and Chinn (1997), among others.
17
An interesting research topic, as suggested by a referee, is to investigate whether the forecasts of thesemodels can generate proﬁtable trading strategies. The issue, which is beyond the scope of the current exercise, would involve obtaining diﬀerent vintages of macro data to use as future variables in generating
forecasts.

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Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

One question that might occur to the reader is whether our results are sensitive tothe out-of-sample period we have selected. In fact, it is possible to improve the performance of the models according to an MSE criterion by selecting a shorter out-ofsample forecasting period. In another set of results (Cheung et al., 2005), we implemented the same exercises for a 1993q1e2000q4 forecasting period, and found somewhat greater success for dollar-based rates according to the MSE criterion, andsomewhat less success along the direction of change dimension. We believe thatthe diﬀerence in results is an artifact of the long upswing in the dollar during the
1990s that gives an advantage to structural models over the no-change forecast embodied in the random walk model when using the most recent 8 years of the ﬂoating
rate period as the prediction sample. This conjecture is buttressed by the fact that the
yen-based exchange rates did not exhibit a similar pattern of results. Thus, in using
fairly long out-of-sample periods, as we have done, we have given maximum advantage to the random walk characterization.

5. Concluding remarks
This paper has systematically assessed the predictive capabilities of models developed during the 1990s. These models have been compared along a number of dimensions, including econometric speciﬁcation, currencies, out-of-sample prediction
periods, and diﬀering metrics. The diﬀerences in forecast evaluations from diﬀerent
evaluation criteria, for instance, illustrate the potential limitation of using a single
criterion such as the popular MSE metric. Clearly, the evaluation criteria could
have been expanded further. For instance, recently Abhyankar et al. (2005) haveproposed a utility-based metric based upon the portfolio allocation problem. Theyﬁnd that the relative performance of the structural model increases when using
this metric. To the extent that this is a general ﬁnding, one can interpret our approach as being conservative with respect to ﬁnding superior model performance.18
At this juncture, it may also be useful to outline the boundaries of this study withrespect to models and speciﬁcations. Firstly, we have only evaluated linear models,eschewing functional nonlinearities (Meese and Rose, 1991; Kilian and Taylor, 2003)
and regime switching (Engel and Hamilton, 1990; Cheung and Erlandsson, 2005).
Nor have we employed panel regression techniques in conjunction with long-run relationships, despite the fact that recent evidence suggests the potential usefulness ofsuch approaches (Mark and Sul, 2001). Further, we did not undertake systems-based
estimation that has been found in certain circumstances to yield superior forecast
performance, even at short horizons (e.g., MacDonald and Marsh, 1997). Sucha methodology would have proven much too cumbersome to implement in the
cross-currency recursive framework employed in this study. Finally, the current
study examines the forecasting performance and the results are not necessarily indicative of the abilities of these models to explain exchange rate behavior. For instance,
18
McCracken and Sapp (2005) forward an encompassing test for nested models. Since not all of ourmodels can be nested in a general speciﬁcation, we do not implement this approach.

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1171

Clements and Hendry (2001) show that an incorrect but simple model may outperform a correct model in forecasting. Consequently, one could view this exercise asa ﬁrst pass examination of these newer exchange rate models.
In summarizing the evidence from this extensive analysis, we conclude that the answer to the question posed in the title of this paper is a bold ‘‘perhaps.’’ That is, theresults do not point to any given model/speciﬁcation combination as being very successful. On the other hand, some models seem to do well at certain horizons, for certain criteria. And indeed, it may be that one model will do well for one exchange rate,
and not for another. For instance, the productivity model does well for the marke
yen rate along the direction of change and consistency dimensions (although not by
the MSE criterion); but that same conclusion cannot be applied to any other exchange rate. Perhaps it is in this sense that the results from this study set the stage
for future research.

Acknowledgements
We thank, without implicating, two anonymous referees, Mario Crucini, Charles
Engel, Jeﬀ Frankel, Fabio Ghironi, Jan Groen, Lutz Kilian, Ed Leamer, Ronald
MacDonald, Nelson Mark, Mike Melvin (Co-Editor), David Papell, Roberto Rigobon, John Rogers, Lucio Sarno, Torsten Sløk, Mark Taylor, Frank Westermann,seminar participants at Academica Sinica, the Bank of England, Boston College,
UCLA, University of Houston, University of Wisconsin, Brandeis University, the
ECB, Kiel, Federal Reserve Bank of Boston, and conference participants at the
NBER Summer Institute, the CES-ifo Venice Summer Institute conference on ‘‘Exchange Rate Modeling’’ and the 2003 IEFS panel on international ﬁnance for helpfulcomments and suggestions. Jeannine Bailliu, Gabriele Galati and Guy Meredith graciously provided data. The ﬁnancial support of faculty research funds of the University of California, Santa Cruz is gratefully acknowledged. The views contained
herein do not necessarily represent those of the IMF or any other organizations
the authors are associated with.

Appendix 1. Data
Unless otherwise stated, we use seasonally adjusted quarterly data from the IMF
International Financial Statistics ranging from the second quarter of 1973 to the lastquarter of 2000. The exchange rate data are end-of-period exchange rates. The output data are measured in constant 1990 prices. The consumer and producer price indices also use 1990 as base year. Inﬂation rates are calculated as 4-quarter log
diﬀerences of the CPI. Real interest rates are calculated by subtracting the lagged inﬂation rate from the 3-month nominal interest rates.
The 3-month, annual and 5-year interest rates are end-of-period constant maturity
interest rates, and are obtained from the IMF country desks. See Chinn and
Meredith (2004) for details. Five-year interest rate data were unavailable for1172

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

Japan and Switzerland; hence data from Global Financial Data http://www.globalﬁndata.com/ were used, speciﬁcally, 5-year government note yields for Switzerlandand 5-year discounted bonds for Japan.
The productivity series are labor productivity indices, measured as real GDP per
employee, converted to indices (1995 Z 100). These data are drawn from the Bankfor International Settlements database.
The net foreign asset (NFA) series is computed as follows. Using stock data foryear 1995 on NFA (Lane and Milesi-Ferretti, 2001) at http://econserv2.bess.tcd.ie/
plane/data.html, and ﬂow quarterly data from the IFS statistics on the current account, we generated quarterly stocks for the NFA series (with the exception of Japan, for which there is no quarterly data available on the current account).
To generate quarterly government debt data we follow a similar strategy. We use
annual debt data from the IFS statistics, combined with quarterly government deﬁcit(surplus) data. The data source for Canadian government debt is the Bank of Canada. For the UK, the IFS data are updated with government debt data from the public sector accounts of the UK Statistical Oﬃce (for Japan and Switzerland we havevery incomplete data sets, and hence no composite models are estimated for thesetwo countries).

Appendix 2. Evaluating forecast accuracy
The DieboldeMariano statistics (Diebold and Mariano, 1995) are used to evaluate the forecast performance of the diﬀerent model speciﬁcations relative to that of
the naive random walk. Given the exchange rate series xt and the forecast series yt,
the loss function L for the mean square error is deﬁned as:Lðyt ÞZðyt  xt Þ2 :ðA1ÞTesting whether the performance of the forecast series is diﬀerent from that of thenaive random walk forecast zt, it is equivalent to testing whether the population
mean of the loss diﬀerential series dt is zero. The loss diﬀerential is deﬁned as
dt ZLðyt Þ  Lðzt Þ:ðA2ÞUnder the assumptions of covariance stationarity and short-memory for dt, thelarge-sample statistic for the null of equal forecast performance is distributed asa standard normal, and can be expressed as
(
d 2p

ðT1Þ
X
tZðT1Þ

lðt=SðTÞÞ

TX dtjtj  d Þðdt  dÞ

)1=2
;

ðA3Þ

tZjtjC1

where lðt=SðTÞÞ is the lag window, S(T ) is the truncation lag, and T is the number ofobservations. Diﬀerent lag-window speciﬁcations can be applied, such as the Barlett

Y.-W. Cheung et al. / Journal of International Money and Finance 24 (2005) 1150e1175

1173

or the quadratic spectral kernels, in combination with a data-dependent lag-selection
procedure (Andrews, 1991).
For the direction of change statistic, the loss diﬀerential series is deﬁned as follows: dt takes a value of one if the forecast series correctly predicts the directionof change, otherwise it will take a value of zero. Hence, a value of d signiﬁcantly larger than 0.5 indicates that the forecast has the ability to predict the direction ofchange; on the other hand, if the statistic is signiﬁcantly less than 0.5, the forecast
tends to give the wrong direction of change. In large samples, the studentized versionof the test statistic,
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ðd  0:5Þ= 0:25=T;ðA4Þ
is distributed as a standard Normal.

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