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Template:Third-party In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts . It was proposed in 2006 by Australian statistician Rob J. Hyndman, who described it as a "generally applicable measurement of forecast accuracy without the problems seen in the other measurements."

The mean absolute scaled error is given by

$\mathrm{M}\mathrm{A}\mathrm{S}\mathrm{E}=\frac{1}{n}\sum _{t=1}^n\left(\frac{\left|e_t\right|}{\frac{1}{n-1}\sum _{i=2}^n|Y_i-Y_{i-1}|}\right)=\frac{\sum _{t=1}^n\left|e_t\right|}{\frac{n}{n-1}\sum _{i=2}^n|Y_i-Y_{i-1}|}$

where the numerator e_t is the forecast error for a given period, defined as the actual value (Y_t) minus the forecast value (F_t) for that period: e_t = Y_t − F_t, and the denominator is the average forecast error of the one-step "naive forecast method", which uses the actual value from the prior period as the forecast: F_t = Y_t−1

This scale-free error metric "can be used to compare forecast methods on a single series and also to compare forecast accuracy between series. This metric is well suited to intermittent-demand seriesTemplate:Clarify because it never gives infinite or undefined values except in the irrelevant case where all historical data are equal.

See also

• Mean squared error
• Mean absolute error
• Mean absolute percentage error

References

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