Evaluation of forecasts in AR models with outliers

The ex-post evaluation of forecasts by the realized forecast errors is an important tool in choosing an adequate model to represent the analyzed time series data and also in comparing competing forecast methods. Measures like the mean squared error MSE and the mean absolute error MAE are frequently used for this purpose. Especially when analyzing data with outliers MSE and MAE may produce misleading results. This paper presents robustified versions MRSE and MRAE of MSE and MAE, respectively. They are much better suited to identify those forecasts which are based on the parameters of the underlying model. This feature is illustrated by a simulation study.