Finite Sample Weighting of Recursive Forecast Errors

This paper proposes and tests a new framework for weighting recursive out-of-sample prediction errors in accordance with their corresponding in-sample estimation uncertainty. In essence, we show how as much information from the sample as possible can be used in the evaluation of prediction accuracy by commencing the forecasts at the earliest opportunity and weighting the prediction errors. We demonstrate through a Monte Carlo study that when only a small sample is available the proposed framework can select the correct model from a set of candidate models considerably more often than the existing standard approach. We also show that the proposed weighting approaches result in tests of equal predictive accuracy which have much better size than the standard approach. An application to a set of exchange rate data highlights relevant differences in the results of tests of predictive accuracy based on the standard approach versus the framework proposed in this paper