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.

See also

• Percentage error
• Mean absolute percentage error
• Mean squared error
• Mean squared prediction error
• Minimum mean-square error
• Squared deviations
• Peak signal-to-noise ratio
• Root mean square deviation
• Errors and residuals in statistics

References

• Khan, Aman U.; Hildreth, W. Bartley (2003). Case studies in public budgeting and financial management. New York, N.Y: Marcel Dekker. ISBN 0-8247-0888-1.
• Waller, Derek J. (2003). Operations Management: A Supply Chain Approach. Cengage Learning Business Press. ISBN 1-86152-803-5.