Middle absolute error

The mean absolute error ( english : Mean Absolute Error , in short: MAE ) is an amount of statistics , the accuracy of that help predictions can be determined.

definition

The mean absolute error is defined as follows:

${\displaystyle MAE={\frac {1}{n}}\textstyle \sum _{i=1}^{n}\displaystyle \mid {\hat {Y}}_{i}-Y_{i}\mid }$,

where the following variables are used:

${\displaystyle n}$: Number of forecast values

${\displaystyle {\hat {Y}}_{i}}$: Predictive values

${\displaystyle Y_{i}}$: Observation values

The MAE is an assessment of a prediction that is size dependent. In order to be able to make comparisons, the variables compared must have the same unit.

The MAE only describes the amount of deviation of the prediction from the observation, but not the direction of deviation (positive or negative deviation). In order to determine this, the mean error or the distortion must be determined.

Normalized mean absolute error

So that the MAE can be designed independently of the order of magnitude, it must be normalized. This is made possible by dividing the MAE either by the sample mean or by the interval length . Either the prediction or the observation can be used to form the mean or the interval length.

The following formula applies to normalization with the mean value:

${\displaystyle nMAE={\frac {MAE}{{\frac {1}{n}}\textstyle \sum _{i=1}^{n}\displaystyle Y_{i}}}}$ or ${\displaystyle nMAE={\frac {MAE}{{\frac {1}{n}}\textstyle \sum _{i=1}^{n}\displaystyle {\hat {Y}}_{i}}}}$

The following formula applies to normalization with the interval length:

${\displaystyle nMAE={\frac {MAE}{Y_{\text{max}}-Y_{\text{min}}}}}$ or ${\displaystyle nMAE={\frac {MAE}{{\hat {Y}}_{\text{max}}-{\hat {Y}}_{\text{min}}}}}$

Whether the mean or the range is used to form the normalized MAE depends on the data to be evaluated. If these are periodic, such as irradiation data from sunlight, it makes more sense to use the interval length.

Individual evidence

1. ↑ 2.5 Evaluating forecast accuracy | OTexts. Retrieved February 28, 2017 (English). 
2. ↑ Forecast Verification. WWRP / WGNE, accessed February 28, 2017 . 
3. ↑ Statistics - CIRPwiki. Retrieved February 28, 2017 (English).