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| In [[statistics]], the '''mean absolute error (MAE)''' is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by
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| :<math>\mathrm{MAE} = \frac{1}{n}\sum_{i=1}^n \left| f_i-y_i\right| =\frac{1}{n}\sum_{i=1}^n \left| e_i \right|.</math>
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| As the name suggests, the mean absolute error is an average of the absolute errors <math>e_i = |f_i - y_i|</math>, where <math>f_i</math> is the prediction and <math>y_i</math> the true value. Note that alternative formulations may include relative frequencies as weight factors.
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| The mean absolute error is a common measure of [[forecast error]] in [[time series analysis]], where the terms "mean absolute deviation" is sometimes used in confusion with the more standard definition of [[mean absolute deviation]]. The same confusion exists more generally.
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| ==Related measures==
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| The mean absolute error is one of a number of ways of comparing forecasts with their eventual outcomes. Well-established alternatives are the [[mean absolute scaled error]] (MASE) and the [[mean squared error]].<ref name="Hyndman2005" /> These all summarize performance in ways that disregard the direction of over- or under- prediction; a measure that does place emphasis on this is the [[mean signed difference]].
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| Where a prediction model is to be fitted using a selected performance measure, in the sense that the [[least squares]] approach is related to the [[mean squared error]], the equivalent for mean absolute error is [[least absolute deviations]].
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| {{refimprove|date=April 2011}}
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| {{morefootnotes|date=April 2011}}
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| ==References==
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| {{Reflist|refs=
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| <ref name="Hyndman2005">Hyndman, R. and Koehler A. (2005). "Another look at measures of forecast accuracy" [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.154.9771&rep=rep1&type=pdf]</ref> | |
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| {{DEFAULTSORT:Mean Absolute Error}}
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| [[Category:Point estimation performance]]
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| [[Category:Statistical deviation and dispersion]]
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| [[Category:Statistical terminology]]
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| [[Category:Time series analysis]]
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