Mean absolute percentage error

Mean absolute percentage error (MAPE) is measure of accuracy in a fitted time series value in statistics, specifically trending. It usually expresses accuracy as a percentage, and is defined by the formula:

$\mbox{M} = \frac{1}{n}\sum_{t=1}^n \left| \frac{A_t-F_t}{A_t}\right|$

where A_t is the actual value and F_t is the forecast value.

The difference between A_t and F_t is divided by the actual value A_t again. The absolute value of this calculation is summed for every fitted or forecast point in time and divided again by the number of fitted points n. This makes it a percentage error so one can compare the error of fitted time series that differ in level.

Although the concept of MAPE sounds very simple and convincing, it has two major drawbacks in practical application:

If there are zero values (which sometimes happens for example in demand series) there will be a division by zero
When having a perfect fit, MAPE is zero. But in regard to its upper level the MAPE has no restriction. When calculating the average MAPE for a number of time series there might be a problem: a few number of series that have a very high MAPE might distort a comparison between the average MAPE of time series fitted with one method compared to the average MAPE when using another method. In order to avoid this problem other measures have been defined, for example the sMAPE (symmetrical MAPE), weighted absolute percentage error (WAPE), real aggregated percentage error (RAPE),or a relative measure of accuracy (ROMA).

The alternative MAPE definition:

Problems can occur when calculating the MAPE value with a series of small denominators. A singularity problem of the form 'one divided by zero' and/or the creation of very large changes in the Absolute Percentage Error, caused by a small deviation in error, can occur.

The difference with the original formula is that each Actual Value (A_t) of the series is replaced by the average Actual Value (Ā_t) of that series. Hence, the distortions are smoothed out. This alternative is still being used for measuring the performance of models that forecast spot electricity prices. ^[1]

References

^ Jorrit Vander Mynsbrugge (2010). Bidding Strategies Using Price Based Unit Commitment in a Deregulated Power Market, K.U.Leuven

Mean absolute percentage error

See also

References