Mean absolute scaled error
Encyclopedia
In statistics
, the mean absolute scaled error (MASE) is a measure of the accuracy of forecast
s . 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."
The mean absolute scaled error is given by
where the numerator et is the forecast error
for a given period, defined as the actual value (Yt) minus the forecast value (Ft) for that period: et = Yt − Ft, 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: Ft = Yt−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.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the mean absolute scaled error (MASE) is a measure of the accuracy of forecast
Forecasting
Forecasting is the process of making statements about events whose actual outcomes have not yet been observed. A commonplace example might be estimation for some variable of interest at some specified future date. Prediction is a similar, but more general term...
s . 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."
The mean absolute scaled error is given by
where the numerator et is the forecast error
Forecast error
In statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest....
for a given period, defined as the actual value (Yt) minus the forecast value (Ft) for that period: et = Yt − Ft, 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: Ft = Yt−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 errorMean squared errorIn statistics, the mean squared error of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or...
- Mean absolute errorMean absolute errorIn statistics, the mean absolute error is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by...
- Mean absolute percentage errorMean Absolute Percentage ErrorMean absolute percentage error is measure of accuracy in a fitted time series value in statistics, specifically trending. It usually expresses accuracy as a percentage, and is defined by the formula:...