mape

MAPE stands for mean absolute percentage error, a statistic used to measure forecast accuracy. It expresses the average of the absolute errors as a percentage of the actual values, making it possible to compare forecast performance across series with different scales. In its common form, for a set of n observations, A_t are the actual values and F_t are the forecasts, MAPE = (100/n) * sum_{t=1..n} |(A_t - F_t)/A_t|. Because the errors are taken in absolute value, MAPE conveys the typical size of forecast errors but not their direction.

MAPE is widely used in time series forecasting, demand planning, and sales forecasting to assess how close forecasts are to observed outcomes and to compare models or methods. It is scale-independent because the errors are measured as a percentage of actual values, but it has notable limitations. If any A_t equals zero, MAPE is undefined; it is also highly sensitive to small actual values, which can inflate the percentage error. The use of the actual value in the denominator means the metric can be biased toward certain patterns, and it treats over- and under-forecasts with different weights in some contexts. It also does not handle outliers well and is not robust to skewed data.

Variants such as symmetric MAPE (sMAPE) attempt to address asymmetry by using a different denominator, for example (100/n) sum 2|A_t - F_t| / (|A_t| + |F_t|). Other measures, like MAE or RMSE, may be preferred when actual units or error direction are important.