Dynamic Forecasting of Monetary Exchange Rate Models:
Evidence from Co-Integration
Jae-Kwang Hwang
University of Alabama
1.Introduction
It has long been believed that nominal exchange rate behavior is well described by the naïve random walk model. This means that there are no systematic economic forces in determining the exchange rates.
Meese and Rogoff (1983) show that none of the structural models (Frenkel-Bilson’s flexible-price monetary model, Dornbush-Frankel’s sticky-price monetary model, Hooper-Morton’s sticky-price asset model) outperform a simple random walk on the basis of the root-mean-squared-error and mean-absolute-error criteria for forecast evaluation. The poor empirical performance of these structural exchange rate models could be the result of simultaneous equation bias, sampling error, stochastic movement in the true underlying parameters, and mis-specification of the underlying models.
But not all writers present results that reject structural exchange rate models. Woo (1985) incorporates a money demand function with a partial adjustment mechanism, and finds that a reformulated monetary approach can outperform the random-walk model in an out of sample forecast exercise. Somanath (1986) also finds that a monetary model with a lagged endogenous variable forecasts better than the naïve random-walk model. Finn (1986) finds that the simple flexible-price monetary model is not supported by the data while the rational-expectations monetary model is supported and performs as well as the random walk model.
MacDonald and Taylor (1993, 1994) also claim some predictive power for the monetary model. MacDonald and Taylor (1993) examine the monetary model of the exchange rate between the deutsche mark and the U.S. dollar over the period January 1976 to December 1990. They find that a dynamic error-correction model outperforms the random- walk forecast at every forecast horizon. MacDonald and Taylor (1994) also find, using a multivariate cointegration technique, that an unrestricted monetary model outperforms the random walk and other models in an out-of-sample forecasting experiment for the sterling-dollar exchange rate.
Mark (1995) presented evidence that long-horizon changes in log nominal exchange rates were predictable using the U.S. dollar price of the Canadian dollar, the deutsche mark, the Swiss franc, and Japanese Yen from 1973:2 to 1991:4. For three out of four exchange rates, the out-of-sample forecasts of the regression outperformed the driftless random walk model at the twelve and sixteen quarter horizons.
Chinn and Meese (1995), using both parametric and non-parametric estimation techniques, examined the forecasting performance of three structural exchange rate models for bilateral exchange rates (Canada, Germany, Japan, and the United Kingdom) relative to the U.S. dollar over March 1973 to December 1990. They showed that three structural exchange rate models could not predict better than a random walk model for short-term horizons. However, for long-term horizons (36 months), these structural models showed more predictive power than the random walk model.
Goldberg and Frydman (1996) found that all the structural exchange rate models considered outperformed the random walk model in the out-of-sample forecast within the separate regimes of stability for the US $ / DM exchange rate over a period March 1973 to March 1988. They also present that the failure of empirical exchange rate models is largely due to the periodic shifts in the long-run relationship governing the exchange rate and macroeconomic fundamentals, i.e. to recurrent shifts in the co-integrating vector.
This paper re-examines the forecasting performance of monetary exchange rate models vis-à-vis the random walk model for the Canadian dollar–U.S. dollar exchange rate over the period January 1980 to December 1996.
This paper uses the multivariate cointegration technique proposed by Johansen (1988) and Johansen and Juselius (1990) to determine the long-run multivariate relationship between the variables. This allows the specification of a dynamic error-correction model of the exchange rates. This technique is superior to the simpler regression-based Engle-Granger (1987) methodology because it fully captures the underlying time series properties of the data, provides estimates of all of the cointegrating vectors that may exist within a vector of variables, and offers a test statistic for the number of cointegrating vectors.
To construct out-of-sample forecasts, the short run dynamic forecasts are made over five forecasting horizons, namely one, three, six, nine, and twelve months for the period 1995:1 to 1996:12. Root mean square error is the principal criterion to test the out- of-sample forecast performance and compared the structural exchange rate models with random walk model.
The organization of this paper is as follows. The next chapter reviews the basic models of exchange rate determination. Chapter 3 discusses the econometric methodology and presents the empirical results. Chapter 4 concludes this paper.