Measure of forecasting quality From Wikipedia, the free encyclopedia
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 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."[1] 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.[2]
The mean absolute scaled error has the following desirable properties:[3]
For a non-seasonal time series,[8] the mean absolute scaled error is estimated by
where the numerator ej is the forecast error for a given period (with J, the number of forecasts), defined as the actual value (Yj) minus the forecast value (Fj) for that period: ej = Yj − Fj, 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),[8] which uses the actual value from the prior period as the forecast: Ft = Yt−1[9]
For a seasonal time series, the mean absolute scaled error is estimated in a manner similar to the method for non-seasonal time series:
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,[8] which uses the actual value from the prior season as the forecast: Ft = Yt−m,[9] 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[1] except in the irrelevant case where all historical data are equal.[3]
When comparing forecasting methods, the method with the lowest MASE is the preferred method.
For non-time series data, the mean of the data () can be used as the "base" forecast.[10]
In this case the MASE is the Mean absolute error divided by the Mean Absolute Deviation.
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