Mean percentage error

In statistics, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.

The formula for the mean percentage error is:


 * $$ \text{MPE} = \frac{100\%}{n}\sum_{t=1}^n \frac{a_t-f_t}{a_t} $$

where $a_t$ is the actual value of the quantity being forecast, $f_t$  is the forecast, and $n$  is the number of different times for which the variable is forecast.

Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result, the formula can be used as a measure of the bias in the forecasts.

A disadvantage of this measure is that it is undefined whenever a single actual value is zero.