Academic journal article Journal of Money, Credit & Banking

Evaluating the Predictability of Exchange Rates Using Long-Horizon Regressions: Mind Your P's and Q's!

Academic journal article Journal of Money, Credit & Banking

Evaluating the Predictability of Exchange Rates Using Long-Horizon Regressions: Mind Your P's and Q's!

Article excerpt

WHEN THE BRETTON Woods Agreement broke down in 1973, most of the large industrialized countries allowed their exchange rates to float against one another. Because this was the first widespread floating of exchange rates in over 50 years, researchers were motivated to develop and estimate empirical models to understand the observed movements in exchange rates. Although preliminary studies had some success at explaining exchange rates, by the early 1980s many of the early successes were being overturned.

One of the most significant negative results was Meese and Rogoff (1983a, 1983b). They analyzed the predictive ability of a series of linear structural exchange rate models and found that none was able to consistently outperform a simple random walk across various exchange rates and forecast horizons. Despite the robustness of this result (e.g., Mark and Sul, 2002, Rapach and Wohar, 2002, Faust, Rogers, and Wright, 2003), there is some evidence of linear structural models outperforming random walk models (e.g., Chinn and Meese, 1995, Mark, 1995, MacDonald and Marsh, 1997). Recent work using non-linear models has also shown promise (e.g., Taylor, Peel, and Sarno, 2001, Cheung, Chinn, and Pascual, 2002, Clarida et al., 2003, Kilian and Taylor, 2003).

Because the original results of Meese and Rogoff (1983a, 1983b) have yet to be convincingly overturned, we investigate the role that the method of inference may have played in determining whether or not structural exchange rate models exhibit superior predictive ability to the random walk model. Much of the existing literature, including Meese and Rogoff (1988) and recent extensions such as Cheung, Chinn, and Pascual (2002), implement a t-type test of equal forecast accuracy recently associated with Diebold and Mariano (1995). Inference is conducted treating these statistics as asymptotically standard normal. As discussed in Section 1, such an approximation is valid when comparing the forecast accuracy of two non-nested models but is invalid when comparing two nested models. Since the structural models typically nest the random walk model, using normal critical values is inappropriate and the resulting p-values do not accurately reflect the significance of the test statistic.

In this paper, we evaluate the predictive ability of linear structural exchange rate models, including the monetary model (Frenkel, 1976, Mussa, 1976, Bilson, 1978), relative to the random walk model with drift using test statistics explicitly designed for an out-of-sample comparison of nested models. Building upon the results in West (1996), McCracken (2000), and Clark and McCracken (2001) derive the limiting distributions of four out-of-sample tests of forecast accuracy and encompassing for one-step ahead forecasts from nested models. Clark and McCracken (2003a) extend their results to allow multi-step forecasts from long-horizon regressions. In related work, Chao, Corradi, and Swanson (2001) derive a test of forecast encompassing that is applicable when one-step ahead forecasts are constructed from either nested or non-nested models. In Section 1 of this paper, we provide an extension of their test that allows for forecasts from longer horizons.

Each of the encompassing tests associated with Chao, Corradi, and Swanson (2001) is asymptotically chi-square and hence asymptotically valid p-values are readily constructed using the relevant tables. Since the remaining tests have nonstandard limiting distributions that are usually dependent upon unknown nuisance parameters, we follow Clark and McCracken (2003a) in using a bootstrap similar to that in Kilian (1999) to estimate asymptotically valid critical values and construct asymptotically valid p-values.

Another reason for using these new tests is that Clark and McCracken (2001, 2003a, 2003b) provide analytical, Monte Carlo, and empirical evidence that some out-of-sample tests of predictive ability have greater power than others. …

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