Maape

MAAPE, or Mean Arctangent Absolute Percentage Error, is a forecast accuracy metric used as an alternative to Mean Absolute Percentage Error (MAPE). It evaluates the closeness of predictions to observed values by taking the arctangent of the absolute percentage error and averaging across observations.

The standard definition is MAAPE = (1/n) sum arctan( |(A_t - F_t) / A_t| ), where A_t is the actual value and F_t is the forecast. The arctangent function bounds each term, producing values between 0 and pi/2 (in radians). Like MAPE, smaller MAAPE indicates better forecasts, and for small errors the arctan of a small ratio behaves approximately linearly, so MAAPE aligns with MAPE in that regime.

Key properties include its boundedness and reduced sensitivity to extremely large percentage errors. By capping the per-item error, MAAPE mitigates the influence of outliers that can overly distort MAPE. However, interpreting MAAPE values in absolute terms is less intuitive than percentage-based errors, and the metric can be affected by how divisions by small actual values are handled.

Practical considerations involve handling cases where A_t is zero. In such instances the ratio is undefined, so common approaches include skipping those observations, substituting a small epsilon, or applying a predefined rule. Some implementations report MAAPE in radians, while others convert to degrees.

MAAPE is used in time-series forecasting and machine learning to provide a robust, scale-free assessment of predictive accuracy. It is often employed alongside MAPE and other metrics to give a more complete picture of forecast performance.