Foreign-Exchange Rate Dynamics: An Empirical Study Using Maximum Entropy Spectral Analysis

Abstract

This study examines whether foreign-exchange rates evolve as a random walk by directly comparing the predictive ability of autoregressive (AR) models of spot rates with that of the random walk. To reduce the influence of model specifications on test results, we neither specify the order of the AR process a priori nor assume that the order is necessarily the same over the entire sample period. For each subperiod, the AR model is estimated by maximum entropy spectral analysis, using Akaike's criterion of final prediction error for optimal order selection. In contrast to standard Box–Jenkins techniques, this analysis neither arbitrarily truncates the data in the time domain beyond the sample period nor imposes periodic extension in the frequency domain, and thus it mitigates against potential structural change in the time series. It is shown that for six currencies, relative to the U.S. dollar, past spot rates are irrelevant for predicting future spot rates, or in other words, spot rates behave as a random walk.

KEY WORDS:

• Spot-exchange rates
• Random walk
• Autoregressive models
• Time series
• Final prediction error