Mean absolute scaled error

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 Hyndman, who described it as a "generally applicable measurement of forecast accuracy without the problems seen in the other measurements."^[1]

The mean absolute scaled error is given by

$\mathrm{MASE} = \frac{1}{n}\sum_{t=1}^n\left( \left|\frac{e_t}{\frac{1}{n-1}\sum_{i=2}^n \left| Y_i-Y_{i-1}\right|}\right| \right)$^[2]

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^[3]

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^{[clarification needed]} because it never gives infinite or undefined values^[1] except in the irrelevant case where all historical data are equal.^[2]

See also

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

References

1. ^ ^{a b} Hyndman, R. J. (2006). "Another look at measures of forecast accuracy", FORESIGHT Issue 4 June 2006, pg46 [1]
2. ^ ^{a b} Hyndman, R. J. and Koehler A. B. (2006). "Another look at measures of forecast accuracy." International Journal of Forecasting volume 22 issue 4, pages 679-688. doi:http://dx.doi.org/10.1016/j.ijforecast.2006.03.001
3. ^ Hyndman, Rob et al, Forecasting with Exponential Smoothing: The State Space Approach, Berlin: Springer-Verlag, 2008. ISBN 978-3-540-71916-8.