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Exchange rate movement has been an important subject of macroeconomic analysis and market surveillance. Despite its importance, forecasting the exchange rate level has been a challenge for academics and market practitioners since the collapse of the Bretton Woods system. Empirical results from many of the exchange rate forecasting models in the literature have not yielded satisfactory results. This paper is constructed for the purpose of comparing the forecast performance of various competing models that have been suggested to forecast exchange rates.
An overview and classifications of models are summarized in Section 2. Section 3 discusses the criteria used to evaluate forecasting performance. The forecasting results are reported in Section 4. Section 5 concludes and indicates why different studies provide different results on the issue. 2. An Overview and Classifications of Models a. Purchasing Power Parity (PPP) Model The PPP model explains the movements of the exchange rate between two economies’ currencies by the changes in the countries’ price levels.
The goods-market arbitrage mechanism will move the exchange rate to equalise prices in the two economies (Madura 2006). Mathematically, the exchange rate determination under the PPP model is expressed as: lnet = lnpt ??? lnpt* where et is the nominal exchange rate, pt and pt* are domestic and foreign prices respectively. The PPP model which is specified as a restrictive error-correction form, following that used in Cheung et al. (2004) is written as: lnet+h ??? lnet = ? o + ? 1 (lnet – ? o ??? ? 1lnp~t) + ? t where p~t is the domestic price level relative to the foreign price level, ? is a zero mean error term, and h is the forecast horizon. The restrictive setup explicitly allows the variation of the exchange rate as a correction of its last-period deviation from a long-run equilibrium b. Uncover Interest Rate Parity (UIP) Model The UIP describes how the exchange rate moves according to the expected returns of holding assets in two different currencies. Ignoring transaction cost and liquidity constraints, the UIP gives an arbitrage mechanism that drives the exchange rate to a value that equalises the returns on holding both the domestic and foreign assets (Madura 2006).
Specifically, if the UIP holds, the arbitrage relationship will give the following expression: Et(lnet+h ??? lnet) = it ??? it* where Et(lnet+h ??? lnet) is the market expectation of the exchange rate return from time t to time t+h; it and it* are the interest rate of the domestic and foreign currencies respectively (Cheung et al. 2004) The UIP model is also tested in the restrictive error-correction form, that is, lnet+h ??? lnet = ? o + ? 1 (lnet – ? o ??? ? 1lni~t) + ? t where i~t is the domestic long-term interest rate relative to that in the foreign country. c. The Structural Models
There are three models selected by Meess and Rogoff (1983) as representatives for this category. They are flexible-price monetary (Frenkel-Bilson) model, the sticky-price monetary (Dornbusch-Frankel) model, and the sticky-price asset (Hooper-Morton) model. The general quasi-reduced form specifications of all three models are: lnet = ao + a1(lnmt ??? lnm*t) + a2(lnyt – lny*t) + a3(lnis – lni*s) + a4(ln? e-ln? e*) + a5TB + a6TB* + u where mt is the domestic money supply, yt is the domestic output, is is the short-term interest rate and ? e is the expected long-run inflation. TB and TB* represent the cumulated U.
S. and foreign trade balances, and u is a disturbance term. The exchange rate exhibits first degree homogeneity in the relative money supplies, i. e a1 = 1 for all the models. The Frenkel-Bilson model, which assumes purchasing power parity, constraints a4 = a5 = a6 = 0. The Dornbusch-Frankel , which allows for slow domestic price adjustment and consequent deviations from PPP, set a5 = a6 = 0. The Hooper-Morton model which allows for changes in the long-run real exchange rate does not constrain any of the coefficients to be zero. d. Univariate and Multivariate Time Series Models
An unconstrained vector autoregression (VAR) was served as a representative multivariate time series model in Meess and Rogoff (1983). In VAR, the contemporaneous value of each variable is regressed against lagged values of itself and all the other variables. The equation is: lnet = ai1st-1 + ai2st-2 +… ainst-n + B’i1 Xt-1 + B’i2 Xt-2+… B’in Xt-n + uit where Xt-1 is a vector of the explanatory variables, lagged j periods. e. The Productivity Model The productivity base model accords a central role to productivity differentials to explaining movements in real, and hence also nominal, exchange rates.
It drops the purchasing power parity assumption for broad price indices, and allows the real exchange rate to depend upon the relative price of nontradables, itself a function of productivity (z) differentials. lnet = ao + a1(lnmt ??? lnm*t) + a2(lnyt – lny*t) + a3(lnis – lni*s) + a4(lnz t -lnz*t) + u f. The Composite Model A typical specification is: lnet = ? o + p^t + ? 5? ^t + ? 6r^t) + ? 7gd^t + ? 8tott + ? 9nfat + ut where ? is the relative price of nontradables, r the real interest rate, gd the government debt to GDP ratio, tot the terms of trade and nfa is the net foreign asset. g. The Monetary Fundamental Model
The fundamental value is, most commonly, given by ft = (lnmt ??? lnm*t) ??? ? (lnyt – lny*t) with f is the long-run equilibrium of the nominal exchange rate determined by the monetary fundamentals. The basic exchange rate equation at forecast horizon k is: Lnet+k ??? Lnet = ? k + ? kzt + vt where zt = ft ??? lnet. This is an error-correction model. If the exchange rate is unpredictable then ? k should be equal to zero. Otherwise, ? k should be positive and should initially increase with the horizon k if the monetary model is useful as a description of the long-run movements in the exchange rate. 3.
Evaluation of Forecast Performance For the purpose of comparison and assessment of the performance of the models, a simple random walk model was employed as a benchmark by Meese and Rogoff (1983) and Cheung et al (2005). The driftless random walk model for an exchange rate in level is specified as et+h = et + ? t (Heaton 2008). Cheung et al (2005) re-assessed exchange rate prediction by comparing the performance of five models: IRP, productivity based, a composite specification, PPP and the sticky-price monetary mode against the random walk. The models were estimated in error correction and first-difference specification.
Moreover, the model performance was evaluated at 1, 4 and 20 quarters forecast horizons by using: – The ratio between the mean squared error (MSE) of the models and a driftless random walk. A value smaller (larger) than one indicates a better performance of the models (random walk). The Diebold-Mariano statistic was used as a test for the null hypothesis of no difference in the accuracy. – The direction of change statistic, which is computed as the number of correct predictions of the direction of change over the total number of predictions. A value above (below) 50% indicates a better (worse) forecasting. Consistency criterion which focuses on the time series properties of the forecast. It is concerned with the long run relative variation between forecasts and actual realizations. Meese and Rogoff (1983) also conducted a research comparing the out of sample accuracy of time series and various structural exchange rate models against the random walk model. Each model was estimated using ordinary least squares, generalized least squares, and Fair’s (1970) instrumental variable techniques. Out of sample accuracy was measured by mean error (ME), mean absolute error (MAE) and root mean squared error (RMSE).
By comparing these errors, it could be ascertained whether a model systematically over- or underpredicts. On the other hand, Faust et al (2003) examined the real-time forecasting performance of standard exchange rate models based on macroeconomic fundamentals for the ? , German mark, CAD$, and Swiss franc versus the US$. An international real time data set was constructed to compare the forecasting performance of the models using different data vintages, real time data on the lagged economic fundamentals and forecasts of future values of fundamentals.
The model used in this paper was Mark’s (1995) monetary fundamental. Abhyankar et al (2005) also employed this model in their paper to investigate whether the economic value of exchange rate forecasts from a fundamental model has greater value than the one of random walk forecasts across a range of horizons. They investigated the ability of a monetary-fundamentals model to predict exchange rates by measuring the economic or utility-based value to an investor who relies on this model to allocate her wealth between two assets that are identical in all respects except the denominated currency.
The focus was on, firstly, how exchange rate predictability affects optimal portfolio choice for investors with a range of horizons up to ten years and secondly whether there is any additional economic value to a utility-maximizing investor who uses exchange rate forecasts from a monetary-fundamental s model relative to an investor who uses forecasts from a naive random walk model. 4. Empirical Results Meese and Rogoff (1983) table 1 gave out the stunning comment that none of the models achieved significantly lower RSME than the random walk model at any horizon.
In other words, the structural models failed to improve on the random walk model in spite of their forecasts were based on realized values of the explanatory variables. Another similar result was obtained for univariate time series models. None of those models improved on the random walk model at any horizon for the dollar/mark rate. However, ME listed in table 2 were much smaller than the corresponding MAE (which yielded the same rankings as RMSE), indicating that the models did not systematically over- or underpredict. The random walk model was somewhat less dominant in ME than in RMSE and MAE.
Similar results were achieved by Cheung et al (2005). Overall, the MSE results were not favourable to the structural models. For the majority cases, the forecasting performance between a structural model and a random walk model could not be differentiated (Table 1). Nevertheless, for direction of change criterion, the results in Table 2 indicated that the structural model forecasts could correctly predict the direction of the change better than the random walk model. The PPP had the highest prediction that gave the correct direction of change, followed by the sticky price, composite, productivity and IRP models.
Interestingly, the cases of correct direction of change prediction appeared to be currency specific and clustered at the long forecast horizon. Only 9% of the total cases of the dollar-based exchange rate forecast series (12% for the yen-based) met the consistency criterion (Table 3 & 4). The implications for optimal portfolio weights when the exchange rate is either a random walk or predictable were reported by Abhyankar et al (2005) in Figure 1 and Table 2. In general, predictability plays an important role in the investor’s choices for all countries and for different values of the coefficient of risk aversion.
Specifically, predictability implies different optimal weights to the foreign asset compared to non-predictability. Especially, predictability using monetary fundamental is of incremental economic value above that for a random walk model. Furthermore, for a low level of risk aversion, the economic value of predictability is not very sensitive to the length of the investment horizon. It is mainly at horizons longer than one year that monetary fundamentals predict future nominal exchange rates better than a naive random walk. Faust et al (2003) Figs 6-9 reported the pure data revisions effect on exchange rate predictability.
Revisions alone have a modest but important effect on the estimated relative RMSE, and lead to substantial increases in the P-values associated with the test of long-horizon forecasting power. While magnitudes vary, the direction of effects is similar across countries and horizons. Relative RMSE rise and ? k fall as the data are more revised, as do the associated P-values. For both real-time and revised-data forecasting, the relative RMSE of the monetary model are generally greater than 1 and increase with horizon (refects the breakdown of the model over this period).
However, for all countries and horizons, the relative RMSE is lower in the real time experiment than in the revised data experiment. Thus, the out of sample predictive power of the monetary model is better using the real time than ex-post revised fundamentals data. 5. Conclusions The Meese and Rogoff (1983) showed the superiority of the random-walk model in out-of-sample exchange-rate forecast. The random walk, in general performed no worse than estimated univariate time series, an unconstrained VAR, or structural models. Faust et al (2003) also supported this when they found considerably less evidence of predictability.
The monetary model generally predicted much less well than the random walk in their experiments. Vice versa, Abhyankar et al (2005) findings concluded that predictability substantially affected both quantitatively and qualitatively the choice between domestic and foreign assets for all currencies and across different levels of risk aversion. Using the information in fundamentals in order to predict the exchange rate out of sample would seem to yield substantial gains. Cheung at al (2005) results, on the other hand, did not point to any given model combinations as being very successful.
Some models seem to do well at certain horizons, for certain criteria and for one exchange rate only, not for another. There would seem to be conflict conclusions reached at this point regarding to the performance of models for exchange rate forecasting. The reason for this may be because of issues concerning the choice of appropriate fundamentals data. Meese and Rogoff (1983) based the forecast on the realized values of the fundamentals in the forecast period. By giving the model actual future data in forming the forecast, Meese and Rogoff seemed to have given the models an arti? ial advantage, making it more noteworthy that the models still generally perform worse than a random-walk model . They also attributed the failure of structural models to world economy’s instability during 1980s, such as the oil price shocks, changes in macroeconomic policy regimes, failure of the models to adequately incorporate other real disturbances, as well as misspecification of the money demand functions. Faust et at (2003), on the other hand, based their study on original release instead of fully-revised data and real-time forecasts in stead of actual future fundamentals.
Abhyankar et at (2005) study focused in on the metric of economic value to an investor, assessing whether there is any economic value to exchange rate predictability in stead of on statistical measures of forecast accuracy, like RMSE, MAE or MSE. Different results achieved by Cheung et al (2005) may be attributed to some boundaries in their study. Firstly, they have only evaluated linear models. Systems-based estimation (Mark and Sul 2001) and panel regression techniques in conjunction with long-run relationships (MacDonald and Marsh 1997) which have been found to be potentially useful in some circumstances have not been employed.
Secondly, their study served on the purpose of examining the forecasting performance. The results were not necessarily an indicator of the abilities of models to explain exchange rate behaviour (Clements and Henry 2001). REFERENCES Abhyankar, A. , Sarno, L. , Valente, G. 2005, ‘Exchange rates and fundamentals: evidence on the economic value of predictability’, Journal of International Economics, 66, p. 325-348. Cheung, Y. , Chinn, M. , Pascual, A. 2005, ‘Empirical exchange rate models of the nineties: are any fit to survive? ‘, Journal of International Money and Finance, 24, p. 1150-1175. Clements, M. P. Hendry, D. F. , 2001, ‘Forecasting with di? erence and trend stationary models’, The Econometric Journal 4, S1eS19. Fair, Ray C. 1970, ‘The estimation of simultaneous equations models with lagged endogenous variables and first order serially correlated errors’, Econometrica 38, 507-516. Faust, J. , Rogers, J. , Wright, J. , 2003, ‘Exchange rate forecasting: the errors we’ve really made’, Journal of International Economics, 60, p. 35-60. Heaton, C. 2008, A Practical Guide to Economic Forecasting, 5th ed, n. p. MacDonald, R. , Marsh, I. , 1997, ‘On fundamentals and exchange rates: a Casselian perspective’.
Review of Economics and Statistics 79, 655e664. Madura, J. 2006, International Financial Management, 9th ed South-Western Publishing, NewYork. Mark, N. C. , 1995, ‘Exchange rates and fundamentals: evidence on long-horizon predictability’, American Economic Review 85, 201 ??? 218. Mark, N. , Sul, D. , 2001. ‘Nominal exchange rates and monetary fundamentals: evidence from a small post Bretton Woods panel’. Journal of International Economics 53, 29e52. Meese, R. , Rogoff, K. , 1983, ‘Empirical exchange rate models of the seventies: do they fit out of sample? ‘ Journal of International Economics, 14, p. 3-24.