On the asymmetry of the symmetric mean absolute percentage error

Several authors have suggested that the use of the mean absolute percentage error (MAPE) as a measure of forecast accuracy should be avoided because they argue it treats forecast errors above the actual observation differently from those below this value. To counter this, the use of a symmetric (or modified) MAPE has been proposed. This paper shows that, in its treatment of negative and positive errors, the proposed modification is far from symmetric, particularly where these errors have large absolute values. It also shows that, under some circumstances, a non-monotonic relationship can occur between the symmetric MAPE and the absolute forecast errors.