A new accuracy measure based on bounded relative error for time series forecasting

TLDR

Many accuracy measures for time series forecasting have been proposed, yet most suffer from issues such as poor outlier resistance and scale dependence. This study introduces the Unscaled Mean Bounded Relative Absolute Error (UMBRAE) to combine the best features of existing measures and address their common shortcomings. The authors evaluate UMBRAE against related metrics by comparing its performance on synthetic and real‑world datasets, following a review of commonly used accuracy measures including SMAPE. Results show that UMBRAE performs as well as or better than other measures on selected criteria, and may be a preferable choice when geometric‑mean‑based relative error metrics are desired.

Abstract

Many accuracy measures have been proposed in the past for time series forecasting comparisons. However, many of these measures suffer from one or more issues such as poor resistance to outliers and scale dependence. In this paper, while summarising commonly used accuracy measures, a special review is made on the symmetric mean absolute percentage error. Moreover, a new accuracy measure called the Unscaled Mean Bounded Relative Absolute Error (UMBRAE), which combines the best features of various alternative measures, is proposed to address the common issues of existing measures. A comparative evaluation on the proposed and related measures has been made with both synthetic and real-world data. The results indicate that the proposed measure, with user selectable benchmark, performs as well as or better than other measures on selected criteria. Though it has been commonly accepted that there is no single best accuracy measure, we suggest that UMBRAE could be a good choice to evaluate forecasting methods, especially for cases where measures based on geometric mean of relative errors, such as the geometric mean relative absolute error, are preferred.