A better measure of relative prediction accuracy for model selection and model estimation

TL;DR

This paper identifies bias in the widely used MAPE forecast accuracy measure and proposes a log accuracy ratio as a superior alternative, especially for heteroscedastic data, with theoretical and simulation validation.

Contribution

It introduces a bias-free relative accuracy measure, the log of the accuracy ratio, and demonstrates its advantages over MAPE for model selection and estimation.

Findings

Log accuracy ratio outperforms MAPE in heteroscedastic data scenarios.

Using the proposed metric leads to models predicting the geometric mean.

Theoretical analysis confirms the metric's desirable properties.

Abstract

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of forecast accuracy in businesses and organizations. It is however, biased: When used to select among competing prediction methods it systematically selects those whose predictions are too low. This is not widely discussed and so is not generally known among practitioners. We explain why this happens. We investigate an alternative relative accuracy measure which avoids this bias: the log of the accuracy ratio: log (prediction / actual). Relative accuracy is particularly relevant if the scatter in the data grows as the value of the variable grows (heteroscedasticity). We demonstrate using simulations that for heteroscedastic data (modelled by a multiplicative error factor) the proposed metric is far superior to MAPE for model selection. Another use for accuracy measures is in fitting parameters to prediction models. Minimum MAPE models do not predict a simple statistic and so theoretical analysis is limited. We prove that when the proposed metric is used instead, the resulting least squares regression model predicts the geometric mean. This important property allows its theoretical properties to be understood.