Error Measures for Generalizing About Forecasting Methods: Empirical Comparisons

Abstract

This study evaluated measures for making comparisons of errors across time series. We analyzed 90 annual and 101 quarterly economic time series. We judged error measures on reliability, construct validity, sensitivity to small changes, protection against outliers, and their relationship to decision making. The results lead us to recommend the Geometric Mean of the Relative Absolute Error (GMRAE) when the task involves calibrating a model for a set of time series. The GMRAE compares the absolute error of a given method to that from the random walk forecast. For selecting the most accurate methods, we recommend the Median RAE (MdRAE) when few series are available and the Median Absolute Percentage Error (MdAPE) otherwise. The Root Mean Square Error (RMSE) is not reliable, and is therefore inappropriate for comparing accuracy across series.

Keywords: Forecast accuracy, M-Competition, Relative absolute error, Theil's U