Mean absolute scaled error

In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts . It was proposed in 2005 by statistician Rob J. Hyndman and Professor of Decision Sciences Anne B. Koehler, 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

$\mathrm {MASE} ={\frac {1}{n}}\sum _{t=1}^{n}\left({\frac {\left|e_{t}\right|}{{\frac {1}{n-1}}\sum _{i=2}^{n}\left|Y_{i}-Y_{i-1}\right|}}\right)={\frac {\sum _{t=1}^{n}\left|e_{t}\right|}{{\frac {n}{n-1}}\sum _{i=2}^{n}\left|Y_{i}-Y_{i-1}\right|}}$

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 series 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