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{{Third-party|date=April 2011}}
In [[statistics]], the '''mean absolute scaled error (MASE)''' is a measure of the [[accuracy]] of [[forecasting|forecast]]s . 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."<ref name="Hyndman2006a" />

The mean absolute scaled error is given by
: <math>\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|}</math><ref name="Hyndman2006" />
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<ref name="Hyndman2008" />

This [[wikt:scalefree|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{{clarify|what is an intermittent-demand series?|date=April 2011}} because it never gives infinite or undefined values<ref name="Hyndman2006a" /> except in the irrelevant case where all historical data are equal.<ref name="Hyndman2006" />

==See also==
* [[Mean squared error]]
* [[Mean absolute error]]
* [[Mean absolute percentage error]]

==References==
{{Reflist|refs=
<ref name="Hyndman2006">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|10.1016/j.ijforecast.2006.03.001}}</ref>
<ref name="Hyndman2006a">Hyndman, R. J. (2006). "Another look at measures of forecast accuracy", FORESIGHT Issue 4 June 2006, pg46 [http://robjhyndman.com/papers/foresight.pdf]</ref>
<ref name="Hyndman2008">Hyndman, Rob et al, ''Forecasting with Exponential Smoothing: The State Space Approach'', Berlin: Springer-Verlag, 2008. ISBN 978-3-540-71916-8.</ref>
}}

{{DEFAULTSORT:Mean absolute scaled error}}
[[Category:Point estimation performance]]
[[Category:Statistical deviation and dispersion]]
[[Category:Statistical terminology]]
[[Category:Time series analysis]]

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