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| {{Refimprove|date=December 2009}}
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| The '''mean absolute percentage error''' ('''MAPE'''), also known as '''mean absolute percentage deviation''' ('''MAPD'''), is a measure of accuracy of a method for constructing fitted time series values in [[statistics]], specifically in [[trend estimation]]. It usually expresses accuracy as a percentage, and is defined by the formula:
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| : <math>\mbox{M} = \frac{100%}{n}\sum_{t=1}^n \left| \frac{A_t-F_t}{A_t}\right|, </math> | |
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| where ''A''<sub>''t''</sub> is the actual value and ''F''<sub>''t''</sub> is the forecast value.
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| The difference between ''A''<sub>''t''</sub> and ''F''<sub>''t''</sub> is divided by the Actual value ''A''<sub>''t''</sub> again. The absolute value in this calculation is summed for every fitted or forecasted point in time and divided again by the number of fitted points ''n''. Multiplying by 100 makes it a percentage error.
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| Although the concept of MAPE sounds very simple and convincing, it has two major drawbacks in practical application:{{cn|date=February 2012}}
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| *If there are zero values (which sometimes happens for example in demand series) there will be a division by zero
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| *When having a perfect fit, MAPE is zero. But in regard to its upper level the MAPE has no restriction.
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| When calculating the average MAPE for a number of time series there might be a problem: a few of the 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).{{cn|date=February 2012}}
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| ==Alternative MAPE definitions==
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| 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.
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| The difference with the original formula is that each Actual Value (A<sub>t</sub>) of the series is replaced by the average Actual Value (Ā<sub>t</sub>) of that series. Hence, the distortions are smoothed out.
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| This alternative is still being used for measuring the performance of models that forecast spot electricity prices.<ref>Jorrit Vander Mynsbrugge (2010). "Bidding Strategies Using Price Based Unit Commitment in a Deregulated Power Market", K.U.Leuven</ref>
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| ==See also==
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| * [[Least absolute deviations]]
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| * [[Mean absolute error]]
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| * [[Mean percentage error]]
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| * [[Symmetric mean absolute percentage error]]
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Mean Absolute Percentage Error}}
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| [[Category:Statistical deviation and dispersion]]
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