forecast performance of exchange rate models revisited

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Forecast performance of exchange rate modelsrevisitedHali J. Edison aa Division of International Finance , Board of Governors of the Federal Reserve System ,Washington, District of Columbia, 20551, USAPublished online: 20 Oct 2008.

To cite this article: Hali J. Edison (1991) Forecast performance of exchange rate models revisited, Applied Economics,23:1, 187-196, DOI: 10.1080/00036849108841063

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Applied Economics, 1991,23, 187-196

Forecast performance of exchange rate models revisited

H A L I J . E D I S O N

Division of International Finance, Board of Governors of the Federal Reserve System, Washington DC 20551, USA

This paper re-evaluates the performance of reduced form exchange rate models by updating the Meese-Rogoff study (1983). This paper confirms earlier tests showing that simple monetary models do not perform well, but it finds more positive results for other monetary models that incorporate more dynamic econometric specifications. A simple error correction monetary model out-forecasts a random walk almost half of the time.

I. I N T R O D U C T I O N model short-run dynamics and long-run equilibrium in the exchange rate market.

With the abandonment of fixed exchange rates in March The paper is organized as follows: Section I1 reconsiders 1973 most of the industrialized countries adopted a system the Meese-Rogoff results. Section 111 discusses an altern- of floating exchange rates, which has been characterized at ative modelling strategy for exchange rates and Section IV times by a high degree of volatility. Over the years there have contains concluding remarks. been many attempts to find a structural model capable of explaining the behaviour of exchange rates. A number of structural models for exchange rates have been proposed,

11. M E E S E - R O G O F F R E S U L T S U P D A T E D . -

but none has proved to be entirely satisfactory. I IA . The models and the method This paper re-evaluates the performance of these reduced-

form exchange rate models by updating the ~ ~ ~ ~ ~ - R ~ ~ ~ f f This section updates the results of Meese-~ogoff (1983, (1983) study, which compared forecast accuracy of time 1988). The models they considered are variants of the series models and structural models of exchange rates for model of exchange rate determination. The quasi-

the dollar/mark, dollar/yen, dollar/pound, and the trade- reduced form Specification of all the models tested below can

weighted dollar exchange rate.' The Meese-Rogoff study be derived l : together with several other studies has revealed that the forecasting accuracy of monetary models is little or no better than random walks in predicting exchange rates. The present paper confirms earlier tests showing that simple monetary models do not perform well, but it finds more positive results for other monetary models that incorporate more dynamic econometric specification^.^

The innovation of this study is that it updates the Meese-Rogoff results on out-of-sample fit of monetary exchange rate models with the most recent data and it utilizes the econometric methods of error correction to

e=a,--a,m+a2m*+a,y-a,y*-a,r+a,r* -a,n+a,n*-a, C T B (1 )

where the superscript*denotes foreign country, e is the logarithm of the exchange rate (in the empirical work e is defined as the foreign exchange price of a dollar, that is, FXi/$), m is the logarithm of the money supply, y is the logarithm of output, r is the short-term interest rate, n is the logarithm of the expected inflation rate, and CTB is the cumulated trade balance.

The Meese-Rogoff exercise estimates three versions of

' I n this paper the exchange rate is quoted as the foreign exchangeJdollar rate. 'There have been a number of studies relating to the predictive performance of exchange rates. Bachus (1984) and Meese and RogoK(1988) have updated and confirmed the original Meese-Rogoff results. There have also been a number of papers making small changes to econometric methodology; e.g. Edison (1985), Woo (1985), Somanath (1986), and Boughton (1987). Other papers by Wolff(1987), Alexander and Thomas (1986) and Schinasi and Swamy (1989) have used time-varying parameter techniques to improve the predictive performance of exchange-rate models.

0003-684619 1 $03.00 + . l 2 0 1991 Chap~not~ and Hall Ltd. 187

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Table l . Root mean square error (RMSE)forecast accuracyfor all modelsa

H . 9. Edison

Step 1 Step 3 Step 6 Step 12

DM/$: Random Walk (Ml) 0.0227 0.0412 0.0492 0.0687 Monetary (M2) 0.0553 0.0647 0.0786 0.1134 Dornbusch-Frankel (M3) 0.0558 0.0706 0.0944 0.1358 Hooper-Morton (M4) 0.0429 0.0552 0.0734 0.1166 Edison-ECM (M5) 0.0243 0.0454 0.0625 0.0933

Yen/$: Random Walk (MI) 0.031 9 0.0696 0.1 195 0.2010 Monetary (M2) 0.1050 0.1353 0.1785 0.2509 Dornbusch-Frankel (M3) 0.0784 0.1094 0.1524 0.2073 Hooper-Morton (M4) 0.0609 0.0957 0.1315 0.1502 Edison-ECM (MS) 0.0332 0.0785 0.1570 0.3735

£/$ : Random Walk (Ml) 0.0230 0.0508 0.0793 0.1539 Monetary (M2) 0.1 127 0.1392 0.1738 0.2556 Dornbusch-Frankel (M3) 0.0965 0.1302 0.1648 0.2 1 70 Hooper-Morton (M4) 0.0583 0.0815 0.1187 0.1711 Edison-ECM (M5) 0.0238 0.0544 0.0851 0.1 644

TW/$: Random Walk (MI) 0.0175 0.0317 0.0412 0.0723 Monetary (M2) 0.0536 0.0648 0.0785 0.1195 Dornbusch-Frankel (M3) 0.0501 0.0641 0.0824 0.107 1 Hooper-Morton (M4) 0.0340 0.0452 0.0629 0.1033 Edison-ECM (M5) 0.0192 0.039 1 0.0622 0.1048

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to November 1976. The end of the sample is November 1980. The number of forecasts for each step is as follows: Step 1 (48 obs.), Step 3 (46 obs.), Step 6 (43 obs.), and Step 12 (37 obs.).

this monetary model reported in Equation 1: (i) Bilson- Frenkel-Mussa (purchasing power parity) which assumes a, = a, =a, = a,, = 0, (ii) Dornbusch-Frankel (slow price adjustment) which assumes a, = a,, = 0, and (iii) Hooper- Morton model which is Equation 1.

Meese-Rogoff estimate all the competing models using monthly data extending back to March 1973, the beginning of the floating rate period. Out-of-sample forecasts are generated for the period December 1976 to November 1980, and for the subperiod December 1978 to November 1980. Each model is initially estimated for each exchange rate using data up to but not including the first forecasting period. Forecasts are then generated at horizons of one, three, six, and twelve months. Then the estimates are updated by one month, always keeping the initial start data, and new forecasts are generated for the four time horizons. T o give the models the benefit of the doubt, Meese-Rogoff

create these forecasts using actual realizations of the exo- genous variables. All models are estimated for the logarithm of the exchange rate and predictions of the exchange rate are performed on the basis of logarithm of the exchange rate to avoid any problems arising from Jensen's i n e q ~ a l i t y . ~ In addition to these equations Meese-Rogoff estimate several time series models. In this paper only the random walk with drift is used in the comparison.

The data are not identical to the Meese-Wogoff (1983) data (Appendix I gives a description of data) because some data sources are no longer available. The data are from March 1973 until October 1987 for the three bilateral exchange rates and until June 1987 for the trade-weighted dollar exchange rate. Therefore, this study not only updates the Meese-Rogoff study, but also reports estimates that replicate their study so differences can be attributed, if necessary, to data sources.

30ut-of-sample forecast accuracy is measured by three statistics: root mean square error, mean absolute error, and mean error. The root mean square error is the principal criterion for comparing forecasts. However, the root mean square error is an inappropriate criterion if exchange rates are governed by non-normal stable Paretian process with infinite variance. The absolute mean error, on the other hand, is a useful criterion when exchange rate distribution has fat tails, even if the variance is finite. The mean error provides another measure of robustness. Also by comparing the mean absolute error and the mean error it is possible to ascertain whether a model systematically over- or underpredicts.

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Table 2. Root mean square error ( R M S E ) forecast accuracy for all modelsa


DM/$: Random Walk (Ml) 0.0234 0.0456 0.0489 0.0660 Monetary (M2) 0.0568 0.0644 0.0720 0.1037 Dornbusch-Frankel (M3) 0.0703 0.0921 0.1275 0.1970 Hooper-Morton (M4) 0.0539 0.0726 0.1020 0.1762 Edison-ECM (MS) 0.0214 0.0375 0.0323 0.0398

Yen/$: Random Walk (Ml) 0.0329 0.0699 0.1 143 0.1 777 Monetary (M2) 0.1097 0.1457 0.193 0.2387 Dornbusch-Frankel (M3) 0.081 5 0.1210 0.1786 0.2287 Hooper-Morton (M4) 0.0779 0.1263 0.1 776 0.21 18 Edison-ECM (M5) 0.0329 0.0788 0.1386 0.2666

L/$ : Random Walk (Ml) 0.0239 0.0482 0.0719 0.1223 Monetary (M2) 0.1334 0.1606 0.1861 0.2035 Dornbusch-Frankel (M3) 0.1162 0.1576 0.1912 0.1641 Hooper-Morton (M4) 0.0708 0.0984 0.1319 0.1464 Edison-ECM (M5) 0.0237 0.0521 0.0706 0.1323

TW/$: Random Walk (M 1) 0.0187 0.0325 0.0266 0.0241 Monetary (M2) 0.0598 0.0703 0.0752 0.0899 Dornbusch-Frankel (M3) 0.0592 0.0777 0.0998 0.1097 Hooper-Morton (M4) 0.0388 0.0512 0.0761 0.1265 Edison-ECM (MS) 0.0158 0.0272 0.0314 0.0564

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to November 1978. The end of the sample is November 1980. The number of forecasts for each step is as follows: Step 1 (24 obs.), Step 3 (22 obs.), Step 6 (19 obs.), and Step 12 (13 obs.).

IIB. The results

Replicating the Meese-Rogofstudy. Tables 1 and 2 report the root mean square error statistics that update the Meese-Rogoff result^.^ The models that have been used to generate these forecasts have been estimated by OLS. In preliminary work these models were estimated with a correction for serial correlation; the results yielded the same ordering of forecast results and consequently are not reported here.5

Table 1 reports the root mean square errors of the four models forecasted over the initial Meese-Rogoff sample, March 1973 to November 1976, with rolling regressions ending in November 1980. Table 2 gives the root mean square errors of the same four models for the Meese-Rogoff initial subsample of March 1973 to November 1978. The reason Meese-Rogoff analyse the two year subperiod is in part due to changes in US intervention policy and in part due to testing whether the competing models perform differently over different time periods.

In general, the results in Tables 1 and 2 replicate the

findings of Meese-Rogoff; that is that the random walk model out-performs the three structural models. The random walk model root mean square error is roughly half that of the Hooper-Morton model, which performs best among the economic models. This out-performance shrinks over the longer forecast horizons but remains substantial. The root mean square error over the 12 step ahead forecast horizon for the random walk models are about a third to a sixth of those for the Hooper-Morton models. In Table 1, the large sample period of Meese-Rogoff, the Yen/$ exchange rate shows that the Hooper-Morton model out-performs the random walk over the longer forecast horizon. This result is not repeated over the shorter subsample forecast period.

Updating the Meese-Rogofstudy. At various times, the path of the dollar has departed from what would be expected on the basis of macroeconomic fundamentals. One of the more dramatic episodes is the period June 1984 to March 1985. The real interest differential moved less in favour of the dollar, yet the dollar appreciated by more than 15%. The purpose of this section is to re-examine the Meese-Rogoff

40ther descriptive statistics - the mean absolute error and the mean error - which were reported in Messe-Rogoff are available in Appendix 11. 'This result is similar to the results reported in the original Meese-Rogoff study.

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Table 3. Root mean square error (RMSE)jbrecast accuracy for all modelsa

H . J . Edison


DM/$: Random Walk (Ml) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (M5)

Yen/$: Random Walk (M 1) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (M5)

£/S : Random Walk (M 1) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (MS)

TW/$: Random Walk (MI) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (M5)

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to March 1985. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate. The number of forecasts for each step is as follows: Step 1 (31/27* obs.), Step 3 (29125' obs.), Step 6 (26/22* obs.), and Step 12 (20/16* obs.). The asterisk indicates the corresponding number of observations for the trade-weighted dollar exchange rate.

findings during this later episode. Furthermore, after March 1985 the dollar depreciated more than 45% until October 1987.

Table 3 reports the root mean squared errors of the four models over the updated sample period. This table relates to the initial sample period of March 1973 to March 1985. Then the equations and the step ahead forecasts are updated until October 1987 (June 1987 for the trade-weighted dollar). This extended sample tests how well the models are able to forecast over the period of large dollar depreciation. Table 3

reduced stopping in May 1984. For both of these samples, on the basis of the root mean square error comparison, the random walk consistently out-performs the structural models. The difference in performance among the models mirrors the previous samples. One striking feature of these results has been the relatively poorer performance of the trade-weighted dollar economic models vis-a-vis the random walk.

shows that the random walk forecasts exchange rate move- I I I . A W A LT M ments better than the three structural models. The one step ahead root mean square errors are all roughly one-third of those for the Hooper-Morton model, which represents the best economic model. The difference in the 12 step ahead forecast during this time period does not erode nearly as rapidly as it did in the earlier samples. From these results, it seems as though the Meese-Rogoff results are robust.

Tables 4 and 5 repeat this exercise over two slightly different sample periods. Table 4 reports results when the initial estimation period is extended to February 1986, and Table 5 gives results when the initial estimation period is

Can we overturn the Meese-Rugof result?

There is a large and growing literature which attempts to overturn the Meese-Rogoff results. That is, there are a number of economists who believe that it is possible to predict movements in the exchange rate. For example, Boughton (1987), Woo (1985), Somanath (1986). and Schinasi and Swamy (1989) have all successfully identified models which at times perform better than the random walk. The common feature in these models tends to be the

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Table 4. Root mean square error ( R M S E ) forecast accuracy for all modelsa


DM/$: Random Walk (Ml) 0.0228 0.0494 0.0887 0.1629 Monetary (M2) 0.3366 0.3737 0.4325 0.5258 Dornbusch-Frankel (M3) 0.2104 0.2456 0.3005 0.3968 Hooper-Morton (M4) 0.0976 0.121 3 0.1601 0.2239 Edison-ECM (M5) 0.0232 0.048 0.0866 0.1655

Yen/$: Random Walk (Ml) 0.0295 0.0596 0.0755 0.1068 Monetary (M2) 0.2446 0.2664 0.2935 0.348 1 Dornbusch-Frankel (M 3) 0.1416 0.1661 0.1841 0.2192 Hooper-Morton (M4) 0.1288 0.1563 0.1747 0.2230 Edison-ECM (M5) 0.0301 0.0593 0.0683 0.0854

E/$ : Random Walk (Ml) 0.0228 0.0549 0.0854 0.1293 Monetary (M2) 0.24 19 0.2669 0.297 1 0.3749 Dornbusch-Frankel (M3) 0.1 557 0.1827 0.21 74 0.2995 Hooper-Morton (M4) 0.1323 0.1649 0.2070 0.3009 Edison-ECM (M5) 0.0200 0.0490 0.0781 0.1215

TW/$: Random Walk (Ml) 0.0208 0.0473 0.0872 0.1737 Monetary (M2) 0.3224 0.3690 0.4395 0.5579 Dornbusch-Frankel (M3) 0.1989 0.2419 0.3080 0.41 95 Hooper-Morton (M4) 0.1898 0.2356 0.3056 0.4347 Edison-ECM (MS) 0.0201 0.0450 0.0820 0.1634

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to February 1986. The end of the sample is October 1987 for the three bilateral rates and June 1487 for the trade-weighted exchange rate. The number of forecasts for each step is as follows: Step 1 (20/16* obs.), Step 3 (18/14* obs.), Step 6 (1511 l* obs.), and Step 12 (9/5* obs.). The asterisk indicates the corresponding number of observations for the trade- weighted dollar exchange rate.

addition of lags to the specification. (Schinasi and Swamy also apply time varying parameters.) In another context Edison (1981) showed that a dynamic error correction specification of exchange rates also tends to out-perform a random walk model for the dollar/pound exchange rate in the 1970s. The reason for the success of these dynamic error correction models is that this specification like the other studies mentioned includes a lagged dependent variable in the error-correction term. Moreover, most of the variables in the monetary model are non-stationary, which leads to problems in inference. Hence the error correction formul- ation which calls for first differencing and using variables with levels helps the econometric specification of the model and furthermore helps in forecasting (e.g. Engle and Yoo, 1987). This type of specification also has the added advan- tage that it incorporates the long-run relationship of PPP which helps the model to forecast better.

In Tables 1-5 a fifth model has been reported and labelled Edison (ECM). Equation 2 represents a very simple error- correction model (Hendry et al., 1984). This model is rather

simple and has not undergone econometric testing.

The major difference between Equation 2 and Equation 1 is that Equation 2 is estimated using both levels and first differences of the variables. The first differences add lag values to the equation and the level term introduces the lagged exchange rate and lagged relative prices (representing PPP).

Tables 1-5 show that this type of model, at least using the forecasting criterion, quite often out-performs the random walk hypothesis. Over all the samples, the error correction model out-forecasts the random walk model at least 40% of the time., This result is most persistent for the Yen/$ and E/$ rates over the later samples. In many cases where the random walk does out-perform the error correction model it does so only marginally. Even when Meese-Rogoff uses a multivariate VAR model, which also incorporates dynamics they could not out-forecast the random walk model.

,Note that I have not tested whether the forecast errors are significantly different from each other.

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Table 5. Root meat1 square error (RMSE)fi)recast accuracy for all models"

M. J . Edison


DM/$ Random Walk (Ml) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (M5)

Yen/$ Random Walk (MI) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (M5)

f /S Random Walk (Ml) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (M5)

TW/$ Random Walk (MI) Monetary (M2) Dornbusch-Frankel (M3) Hooper-Morton (M4) Edison-ECM (M5)

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to May 1984. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate. The number of forecasts for each step is as follows: Step 1 (41137' obs.), Step 3 (39/35* obs.), Step 6 (36132' obs.), and Step 12 (30126' obs.). The asterisk indicates the corresponding number of observations for the trade- weighted dollar exchange rate.

1V. C O N C L U S I O N A P P E N D I X I

The empirical performance of exchange rate models has been widely criticized in recent years. Meese and Rogoff have shown that none of the popular monetary exchange rate models performs better than a random walk in predicting the nominal exchange rate. The main result in the present paper is that following a dynamic econometric methodology it is possible to build exchange rate models that out-perform a random walk model. Furthermore, in the past year there have been several attempts at improving exchange rate forecasts using non-linear models but the results have been extremely disappointing.' Non-linear models do not tend to forecast better than a random walk model. In contrast, the results reported here suggest some hope in using dynamic specification to improve exchange rate models. This result casts some doubt on those who claim that standard observ- able macroeconomic variables are not capable of explaining, much less predicting, the short-run movements in the exchange rate.

The data are sampled monthly from March 1973 to October 1987 (the trade-weighted data only extend until June 1987). All data are non-seasonally adjusted and come from publicly available sources. Exchange rate and interest rate data are from the Federal Reserve database. The data are monthly averages unless noted otherwise. Exchange rates are quoted FXi/$ rates (a rise in the exchange rate implies an appreci- ation of the dollar) and are New York noon bid rates. The short-term interest rates are interbank rates and the long- term rates pertain to 5 to 10 year maturities. The trade balance, industrial production, CPH indices, and money supplies (M l ) are from national sources. The weights used to determine the trade-weighted data are as follows: Belgium (0.064), Canada (0.09 l), France (0.13 l), Germany (0.208), Italy (0.090), Japan (0.136), Netherlands (0.083), Sweden (0.042), Switzerland (0.036), and the United Kingdom (0. l 19).

'See for example the papers by Meese and Rose (1989) and Diebold and Nason (in press).

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Forecast performance of exchange rate models revisited 193

A P P E N D I X I 1 Table A2. Mean error (ME) step ahead vectors (for all modelsa)

Table A l. Absolute mean error (AME) step ahead vectors (for all modelsa)


DM/$ Random Walk (M1) Monetary (M2) Dornbusch-Frankel

(M3) Hooper-Morton (M4) Edison-ECM (M5)

Yen/$ M 1 M2 M3 M4 M5

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to November 1976. The end of the sample is November 1980.

Step I Step 3 Step 6 Step 12

DM/% Random Walk (Ml) Monetary (M2) Dornbusch-Frankel

(M31 Hooper-Morton (M4) Edison-ECM (M5)

p-


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Table A3. Absolute mean error (AME) step ahead vectors (for all models")


DM/$ Random Walk (MI) 0.0177 0.0359 0.0405 0.0480 Monetary (M2) 0.0432 0.0512 0.0560 0.0839 Dornbusch-Frankel 0.0558 0.0734 0.0938 0.1791

(M3) Hooper-Morton (M4) 0.0405 0.061 8 0.0921 0.1659 Edison-ECM (MS) 0.01 67 0.0307 0.0253 0.0341

TW/$ M1 0.0143 0.0259 0.0194 0.0190 M2 0.0430 0.0532 0.0587 0.0728 M3 0.0450 0.0653 0.0823 0.0927 M4 0.0266 0.0376 0.059 0.1 199 M5 0.01 19 0.0204 0.0265 0.0420


Table A4. Mean error (ME) step ahead vectors (for all models")


DM/$ Random Walk (M 1) Monetary (M2) Dornbusch-Frankel

(M31 Hooper-Morton (M4) Edison-ECM (MS)

Yen/$ M1 M2 M3 M4 M5

E/$ M1 M2 M3 M4 M5

TW/$ M 1 M2 M3 M4 M5




DM/$ Random Walk (M 1) Monetary (M2) Dornbusch-Frankel



E/$ M1 M2 M3 M4 M5

TW/% M 1 M2 M3 M4 M5

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to March 1985. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate.



DM/$ Random Walk (Ml) Monetary (M2) Dornbusch-Frankel


"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to March 1985. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate.

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Table A9. Ahsolute mean error (AM E) step ahead vectors (for all models")

Step 1 Step 3 Step 6 Step 12 Step 1 Step 3 Step 6 Step 12


043) Hooper-Morton (M4) Edison-ECM (M5)



(M3) Hooper-Morton (M4) Edison-ECM (MS)


f/$ M1 M2 M3 M4 M5

TW/$ M1 M2 M3 M4 M5

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to February 1986. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate.

Table A8. Mean error (ME) step ahead vectors (for all modelsa)

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to May 1984. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate.


Step 1 Step 3 Step 6 Step 12 Step 1 Step 3 Step 6 Step 12

DM/$ Random Walk (MI) Monetary (M2) Dornbusch-Frankel

043) Hooper-Morton (M4) Edison-ECM (M5)


f /$ M1 M2 M3 M4 M5

TW/$ M 1 M2 M3 M4 M5




f l$ M1 M2 M3 M4 M5

TW/$ M1 M2 M3 M4 M5

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to February 1986. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate.

p-pp

"Forecasts for all models are based on rolling regressions. Initial sample period is March 1973 to May 1984. The end of the sample is October 1987 for the three bilateral rates and June 1987 for the trade-weighted exchange rate.

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H . J . Edison

ACKNOWLEDGEMENTS

I would like to thank Stephen Scott and Carolyn Litynski for research assistance, and to thank Patrick Decker, Bill Helkie, Karen Johnson, and Linda Kole for guidance on data sources. This paper represents the views of the author and should not be interpreted as representing the views of the Board of Governors of the Federal Reserve System.

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forecast performance of exchange rate models revisited

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