SUMMARYWe propose new methods for comparing the out-of-sample forecasting performance of two competing models in the presence of possible instabilities. The main idea is to develop a measure of the relative local forecasting performance for the two models, and to investigate its stability over time by means of statistical tests. We propose two tests (the Fluctuation test and the One-Time Reversal test) that analyze the evolution of the models' relative performance over historical samples. In contrast to previous approaches to forecast comparison, which are based on measures of global performance, we focus on the entire time path of the models' relative performance, which may contain useful information that is lost when looking for the model that forecasts best on average. We apply our tests to the analysis of the time variation in the out-of-sample forecasting performance of monetary models of exchange rate determination relative to the random walk.

The main goal of this article is to provide an answer to the question: "Does anything forecast exchange rates, and if so, which variables?". It is well known that exchange rate ‡uctuations are very di¢ cult to predict using economic models, and that a random walk forecasts exchange rates better than any economic model (the Meese and Rogo¤ puzzle). However, the recent literature has identi…ed a series of fundamentals/methodologies that claim to have resolved the puzzle. This article provides a critical review of the recent literature on exchange rate forecasting and illustrates the new methodologies and fundamentals that have been recently proposed in an upto-date, thorough empirical analysis. Overall, our analysis of the literature and the data suggests that the answer to the question: "Are exchange rates predictable?" is, "It depends" -on the choice of predictor, forecast horizon, sample period, model, and forecast evaluation method. Predictability is most apparent when one or more of the following hold: the predictors are Taylor rule or net foreign assets, the model is linear, and a small number of parameters are estimated. The toughest benchmark is the random walk without drift.

and seminar participants at the University of Washington for comments. We are also grateful to various staff members of the Reserve Bank of Australia, the Bank of Canada, the Reserve Bank of New Zealand, and the IMF for helpful discussions and for providing some of the data used in this paper. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.