Assessing the forecasting accuracy of alternative nominal exchange rate models: the case of long memory

This paper presents an autoregressive fractionally integrated moving-average (ARFIMA) model of nominal exchange rates and compares its forecasting capability with the monetary structural models and the random walk model. Monthly observations are used for Canada, France, Germany, Italy, Japan and the United Kingdom for the period of April 1973 through December 1998. The estimation method is Sowell's (1992) exact maximum likelihood estimation. The forecasting accuracy of the long-memory model is formally compared to the random walk and the monetary models, using the recently developed Harvey, Leybourne and Newbold (1997) test statistics. The results show that the long-memory model is more efficient than the random walk model in steps-ahead forecasts beyond 1 month for most currencies and more efficient than the monetary models in multi-step-ahead forecasts. This new finding strongly suggests that the long-memory model of nominal exchange rates be studied as a viable alternative to the conventional models. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  K. West.  A Standard Monetary Model and the Variability of the Deutschemark-Dollarexchange Rate , 1986 .

[2]  Kenneth J. Singleton,et al.  On Unit Roots and the Empirical Modeling of Exchange Rates , 1982 .

[3]  Ying-Wong Cheung,et al.  A search for long memory in international stock market returns , 1995 .

[4]  Fluctuations in the Dollar : A Model of Nominal and Real Exchange Rate Determination , 1980 .

[5]  Fred R. Kaen,et al.  R/S analysis of foreign exchange rates under two international monetary regimes , 1982 .

[6]  C. Granger.  Long memory relationships and the aggregation of dynamic models , 1980 .

[7]  Benjamin J. C. Kim,et al.  Cointegration and the long-run forecast of exchange rates , 1995 .

[8]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[9]  Jeremy P. Smith,et al.  Comparing the bias and misspecification in ARFIMA models , 1997 .

[10]  P. Robinson.  Efficient Tests of Nonstationary Hypotheses , 1994 .

[11]  Francis X. Diebold,et al.  The Review of Economics and Statistics VOL . LXXIII FEBRUARY 1991 NUMBER 1 IS CONSUMPTION TOO SMOOTH ? LONG MEMORY AND THE DEATON PARADOX , 2008 .

[12]  Kenneth S. Rogoff,et al.  Exchange rate models of the seventies. Do they fit out of sample , 1983 .

[13]  M. Taqqu,et al.  Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series , 1986 .

[14]  S. Porter-Hudak.  An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregates , 1990 .

[15]  Tim Bollerslev,et al.  The long memory of the forward premium , 1994 .

[16]  Glenn D. Rudebusch,et al.  Long Memory and Persistence in Aggregate Output , 1989, Business Cycles.

[17]  F. Diebold,et al.  Real Exchange Rates under the Gold Standard , 1991, Journal of Political Economy.

[18]  L. Gil‐Alana.  Testing of Seasonal Fractional Integration in UK and Japanese Consumption and Income , 2000 .

[19]  A. Lo.  Long-Term Memory in Stock Market Prices , 1989 .

[20]  A. Lo.  Long-Term Memory in Stock Market Prices , 1991 .

[21]  R. Meese.  Testing for Bubbles in Exchange Markets: A Case of Sparkling Rates? , 1986, Journal of Political Economy.

[22]  Christian C. P. Wolff.  Time-Varying Parameters and the Out-of-Sample Forecasting Performance of Structural Exchange Rate Models , 1987 .

[23]  Fallaw Sowell.  Maximum likelihood estimation of stationary univariate fractionally integrated time series models , 1992 .

[24]  J. Frenkel.  A Monetary Approach To The Exchange Rate: Doctrinal Aspects And Empirical Evidence , 1976 .

[25]  K. Lai,et al.  Long memory and nonlinear mean reversion in Japanese yen-based real exchange rates , 2001 .

[26]  Glenn D. Rudebusch,et al.  On the Power of Dickey-Fuller Tests against Fractional Alternatives , 1991, Business Cycles.

[27]  Paul Newbold,et al.  Testing the equality of prediction mean squared errors , 1997 .

[28]  J. Frenkel,et al.  The Economics of exchange rates : selected studies , 1978 .

[29]  Kenneth A. Froot,et al.  Chartists, Fundamentalists and the Demand for Dollars , 1991 .

[30]  R. Dornbusch.  Expectations and Exchange Rate Dynamics , 1976, Journal of Political Economy.

[31]  Ying-Wong Cheung,et al.  Long Memory in Foreign-Exchange Rates , 1993 .

[32]  Uwe Hassler,et al.  Long Memory in Inflation Rates: International Evidence , 1995 .

[33]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[34]  Ying-Wong Cheung,et al.  A Fractional Cointegration Analysis of Purchasing Power Parity , 1993 .

[35]  P. A. V. B. Swamy,et al.  The out-of-sample forecasting performance of exchange rate models when coefficients are allowed to change , 1987 .

[36]  Jeffrey A. Frankel,et al.  On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials , 1979 .

[37]  Mark P. Taylor,et al.  The use of technical analysis in the foreign exchange market , 1992 .