Mean absolute error

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

$\mathrm{MAE} = \frac{1}{n}\sum_{i=1}^n \left| f_i-y_i\right| =\frac{1}{n}\sum_{i=1}^n \left| e_i \right|.$

As the name suggests, the mean absolute error is an average of the absolute errors e_i = f_i − y_i, where f_i is the prediction and y_i the true value. Note that alternative formulations may include relative frequencies as weight factors.

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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.^[1] 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.

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.

References

1. ^ Hyndman, R. and Koehler A. (2005). "Another look at measures of forecast accuracy" [1]