The MAPE (mean absolute percentage error) is a popular measure for forecast accuracy and is defined as $$ \text{MAPE} = 100\text{mean}(|y_t - \hat{y}_t|/|y_t|) $$ where $y_t$ denotes an observation and $\hat{y}_t$ denotes its forecast, and the mean is taken over $t$. Armstrong (1985, p.348) was the first (to my knowledge) to point out the asymmetry of the MAPE saying that “it has a bias favoring estimates that are below the actual …