Another look at measures of forecast accuracy

International Journal of Forecasting (2006). 22(4), 679-688.

Rob J. Hyndman1 and Anne B. Koehler2

  1. Department of Econometrics and Business Statistics, Monash University, VIC 3800, Australia.
  2. Department of Decision Sciences and Management Information Systems, Miami University, Oxford, OH 45056, USA.

Abstract: We discuss and compare measures of accuracy of univariate time series forecasts. The methods used in the M-competition and the M3-competition, and many of the measures recommended by previous authors on this topic, are found to be degenerate in commonly occurring situations. Instead, we propose that the mean absolute scaled error become the standard measure for comparing forecast accuracy across multiple time series.

Keywords: forecast accuracy, forecast evaluation, forecast error measures, M-competition, mean absolute scaled error.

Sample calculations: Excel spreadsheet showing MASE calculation for the “product C” series.

Data: Data used in examples.

Online article

Preprint version