In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts. It is the mean absolute error of the forecast values, divided by the mean absolute error of the in-sample one-step naive forecast. It was proposed in 2005 by statistician Rob J. Hyndman and decision scientist 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 has favorable properties when compared to other methods for calculating forecast errors, such as root-mean-square-deviation, and is therefore recommended for determining comparative accuracy of forecasts.

The mean absolute scaled error has the following desirable properties:

For a non-seasonal time series, the mean absolute scaled error is estimated by

where the numerator e_j is the forecast error for a given period (with J, the number of forecasts), defined as the actual value (Y_j) minus the forecast value (F_j) for that period: e_j = Y_j − F_j, and the denominator is the mean absolute error of the one-step "naive forecast method" on the training set (here defined as t = 1..T), which uses the actual value from the prior period as the forecast: F_t = Y_t−1

For a seasonal time series, the mean absolute scaled error is estimated in a manner similar to the method for non-seasonal time series:

${\displaystyle \mathrm {MASE} =\mathrm {mean} \left({\frac {\left|e_{j}\right|}{{\frac {1}{T-m}}\sum _{t=m+1}^{T}\left|Y_{t}-Y_{t-m}\right|}}\right)={\frac {{\frac {1}{J}}\sum _{j}\left|e_{j}\right|}{{\frac {1}{T-m}}\sum _{t=m+1}^{T}\left|Y_{t}-Y_{t-m}\right|}}}$

The main difference with the method for non-seasonal time series, is that the denominator is the mean absolute error of the one-step "seasonal naive forecast method" on the training set, which uses the actual value from the prior season as the forecast: F_t = Y_t−m, where m is the seasonal period.

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 (a data set containing a large amount of zeros) because it never gives infinite or undefined values except in the irrelevant case where all historical data are equal.