Biasedness of forecasts errors for intermittent demand data

Abstract

Purpose: Intermittent demand is defined as infrequent or sporadic. Many forecasting errors are inappropriate for intermittent data. In some periods, there could be no demand, so division by zero must be avoided. Usually, forecasts are computed for many products; therefore, errors should be scale-independent (or relative). Many ex-post forecast errors, such as MASE (Mean Absolute Scaled Error) or MAE (Mean Absolute Error), indicate as best very low forecasts, sometimes even zero forecasts. Therefore, many researchers think that measures taking into account stock and consumer service levels should be used instead of conventional forecasts. It might suggest that typical forecast errors are useless for intermittent data. In this article, the contradictory hypothesis is verified. It is stated that only unbiased forecast errors should be used if the conclusions are to be correct. Design/Methodology/Approach: Definition of unbiased forecast error is proposed and verified for popular forecast errors, such as ME (Mean Error), MSE (Mean Square Error), MAE, or MASE. The theoretical properties of these errors are considered concerning their biasedness. Forecasts are made based on Croston’s and TSB methods, but also average and median were used as forecasting methods to emphasize conclusions. Findings: In the empirical example, forecast errors are computed for intermittent demand times series to verify theoretical conclusions. The general conclusion is that only unbiased forecast errors provide proper indications according to forecast accuracy. This finding is true in general, not only for intermittent demand. Practical Implications: Presented considerations might be useful for enterprises dealing with intermittent demand forecasting such as distribution centers, warehouse centers, and so on. Originality/value: To the author’s knowledge, forecast error bias was not analyzed before in the literature. A new forecast error is proposed, which was named RMSSE (Root Mean Square Scaled Error).