Revisiting the Martingale Hypothesis for Exchange Rates

Abstract

Many structural models have attempted to explain the behaviour of exchange rates under the floating rate regime. Meese and Rogoff (1983) found that a random walk model performs at least as well as various structural and time series models for exchange rates in terms of out-of-sample forecast. But, the random walk model is often rejected when the variance-ratio test is employed. In this paper, we attempt to resolve these apparently contradictory empirical findings. Our view is that (i) when a model successfully passes a battery of independent out-of-sample tests, it is likely to describe the true process, and (ii) apart from the fact that the variance-ratio test is inherently an in-sample test, it might be possible that researchers fail to take into account all the relevant characteristics of the process when conducting the variance-ratio test. One characteristic we will focus on in this paper is possible structural breaks in the exchange rate process. We consider a simple random walk process, a special case of the Martingale model, which exhibits a deterministic break in its drift term, for instance, from positive to negative. This particular example can be a plausible model for a time series on exchange rates which displays a persistent currency appreciation period followed by a long depreciation era. We demonstrate both theoretically and by simulation that when the standard variance-ratio test is applied to this process, the phenomenon of spurious rejections of the Martingale hypothesis can occur. We discuss some implication of this finding on the previously uncovered empirical evidence against the Martingale hypothesis for exchange rates. We propose a modification of the variance-ratio test taking into account structural breaks in the process. We have found that the standard tests strongly reject the Martingale hypothesis while our tests do not. Our empirical findings strongly indicate that rejecting the Martingale hypothesis by the standard variance-ratio tests might have been induced by failing to incorporate structural breaks into the testing procedure.