A new metric of absolute percentage error for intermittent demand forecasts

TLDR

MAPE is a widely used, scale‑independent, interpretable forecast accuracy metric, but it yields infinite or undefined values when actuals are zero or near zero. This paper introduces the mean arctangent absolute percentage error (MAAPE) to overcome that limitation. MAAPE is derived by treating the absolute percentage error as an angle via the arctangent function, thereby preserving MAPE’s philosophy while avoiding division by zero and providing bounded influence for outliers. Theoretical analysis and experiments on simulated and real‑world data demonstrate MAAPE’s desirable properties and practical advantages over MAPE.

Abstract

The mean absolute percentage error (MAPE) is one of the most widely used measures of forecast accuracy, due to its advantages of scale-independency and interpretability. However, MAPE has the significant disadvantage that it produces infinite or undefined values for zero or close-to-zero actual values. In order to address this issue in MAPE, we propose a new measure of forecast accuracy called the mean arctangent absolute percentage error (MAAPE). MAAPE has been developed through looking at MAPE from a different angle. In essence, MAAPE is a slope as an angle, while MAPE is a slope as a ratio, considering a triangle with adjacent and opposite sides that are equal to an actual value and the difference between the actual and forecast values, respectively. MAAPE inherently preserves the philosophy of MAPE, overcoming the problem of division by zero by using bounded influences for outliers in a fundamental manner through considering the ratio as an angle instead of a slope. The theoretical properties of MAAPE are investigated, and the practical advantages are demonstrated using both simulated and real-life data.