Marketing Papers

Document Type

Journal Article

Date of this Version



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.


Postprint version. Published in International Journal of Forecasting, Volume 8, Issue 1, June 1992, pages 69-80.
Publisher URL:


forecast accuracy, M-Competition, relative absolute error, Theil's U

Included in

Marketing Commons



Date Posted: 14 June 2007

This document has been peer reviewed.