Foreign Currency Forecasts: A Combination Analysis


This paper uses a large variety of different models and examines the predictive performance of these exchange rate models by applying parametric and non-parametric techniques. For forecasting, we will choose that predictor with the smallest root mean square forecast error (RMSE). The results show that the better model is equation (34), but none of them gives a perfect forecast. At the end, error correction versions of the models will be fit so that plausible long-run elasticities can be imposed on the fundamental variables of each model.




Many economic time series do not have a constant mean and most exhibit phases of relative tranquility followed by periods of high volatility. Casual inspection of exchange rates and many other economic time series data suggest that they do not have a constant mean and variance. (A stochastic variable with a constant variance is called homoscedastic, as opposed to heteroscedastic.) For series exhibiting volatility, the unconditional variance may be constant even though the variance during some periods is unusually large. The trends displayed by some variables may contain deterministic or stochastic components. In our analysis, it actually makes a great deal of difference if a series is estimated and forecasted under the hypothesis of a deterministic versus a stochastic trend.

By graphing the different exchange rates, we can illustrate their behavior just by looking at the fluctuation of these rates over time. Of course, formal testing is necessary to substantiate any first impressions.

The first visual pattern is that these series are not stationary, in that the sample means do not appear to be constant and there is a strong appearance of heteroscedasticity. It is hard to maintain that these series do have a time-invariant mean. They do not contain a clear trend. The dollar/pound exchange rate shows no particular tendency to increase or decrease. The dollar seems to go through sustained periods of appreciation and then depreciation without a tendency of reversion to a long-run mean. This type of “random walk” behavior is typical of non- stationary series.

Any shock to the series displays a high degree of persistence. Notice that the $/£ exchange rate experienced a violently upward surge in 1980 and remained at this higher growth for nearly four years; it had almost returned to its previous level after nine years. The volatility of these series is not constant over time. (Such series are called conditionally heteroscedastic if the unconditional or long-run variance is constant but there are periods in which the variance is relatively high.) Some exchange rates series share co- movements with other series. Large shocks to the U.S. appear to be timed similarly to those in the U.K. and Canada. The presence of such co- movements should not be too surprising. We might expect that the underlying economic forces affecting the U.S. economy also affect the economy internationally.

In conventional econometric models, the variance of the disturbance term is assumed to be constant. However, the data demonstrate that our series in question exhibit periods of unusually large volatility followed by periods of relative tranquility. In such circumstances, the assumption of a constant variance (homoscedasticity) is inappropriate.

As an asset holder denominated in one currency, you might want to forecast the exchange rate and its conditional variance over the holding period of the asset. The unconditional variance (i.e., the long- run forecast of the variance) would be unimportant if you plan to buy the asset at t and sell it at t+1. Kallianiotis (1995) and Taylor (1995) provide a recent survey and review of the literature on exchange rate economics. Chinn and Meese (1995) examine the performance of four structural exchange rate models.

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