How to Estimate Forecasting Quality: A System-Motivated Derivation of Symmetric Mean Absolute Percentage Error (SMAPE) and Other Similar Characteristics

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Hung T. Nguyen, New Mexico State University - Main CampusFollow
Rujira Ouncharoen, Chiang Mai UniversityFollow

Publication Date

7-2014

Comments

Technical Report: UTEP-CS-14-53

Abstract

When comparing how well different algorithms forecast time series, researchers use an average value of the ratio |x-y|/(|x|+|y|)/2), known as the Symmetric Mean Absolute Percentage Error (SMAPE). In this paper, we provide a system-motivated explanation for this formula. We also explain how this formula explains the use of geometric mean to combine different forecasts.