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A Comparison of Model Averaging Methods in Foreign Exchange Prediction

Statistical learning theory predicts, and empirical results confirm, that averaging the predictions of several learned models will often result in higher accuracies than using only the single “best” model. However, the averaging methods typically used in practice (e.g., assigning uniform weights to all models) differ from the theoretical Bayesian optimum, which is to weight each model by its posterior probability. In this extended abstract, uniform and Bayesian weighting are compared on a practical task, some problems of the latter are identified, and a new heuristic weighting scheme is proposed, leading to improved performance. The application domain used was that of foreign exchange prediction, where the goal is to maximize the return from investing in a foreign currency by predicting whether it will rise or fall against the U.S. dollar. An approach that is used by some traders, and that has been validated by large-scale empirical studies (LeBaron 1991), involves the use of so-called technical rules of the form “If the s-day moving average of the currency’s exchange rate rises above the t-day one, buy; else sell.” The choice of s and t, with t > s, can be made empirically. The fact that there is clearly no single “right” rule suggests that the use of multiple models is appropriate. Given a realistic maximum value for t (weeks or months), the number of possible rules is small enough that Bayesian averaging can be applied in its optimal form, averaging all models in the space, and not just a selected few. Tests were conducted using daily data on four currencies for the years 1973-87, from the Chicago Mercantile Exchange. The first ten years were used for training (2341 examples) and the remaining five for testing. A maximum t of two weeks was used. The results, in terms of the five-year return on investment obtained, are shown in the table above. The first column shows the result of buying the foreign currency on the first day and holding it throughout the five years. The second column corresponds to applying the single best rule, and is a clear improvement over the former. The remaining columns show the results of applying various model averaging methods.