MAPEs

MAPEs, or mean absolute percentage errors, are metrics used to assess forecast accuracy by expressing errors as percentages of the actual values. The most common form is MAPE, defined as MAPE = (100/n) * sum_t |A_t - F_t| / |A_t|, where A_t is the actual value and F_t is the forecast for period t. A lower MAPE indicates closer forecasts. Because the errors are in percentage terms, MAPE is easy to interpret and can facilitate comparisons across series with different scales.

MAPE has several caveats. It is undefined when any actual value is zero, and even near-zero actuals can produce extremely large percentages, biasing the metric. Percentage errors also emphasize errors on small actuals and can be distorted by outliers. Additionally, MAPE does not treat over- and under-forecasting identically in all contexts, and it can penalize forecasts differently across series with varying magnitudes.

Variants and alternatives are common. Symmetric MAPE (sMAPE) uses 2|F - A| / (|A| + |F|) to mitigate infinite values and bias from small actuals. Mean Arctangent Absolute Percentage Error (MAAPE) applies arctan to the absolute percentage error to dampen outliers. In practice, zero actuals may be handled by substituting a small epsilon, or analysts may opt for other metrics such as MAE or RMSE depending on the application.

Applications: MAPEs are widely used in business forecasting, economics, and time-series model evaluation to compare competing models or methods. Related metrics include MAE, MSE, RMSE, and sMAPE.