Robust forecast combinations

Forecast outliers commonly occur in economic, financial, and other areas of forecasting applications. In the literature of forecast combinations, there have been only a few studies exploring how to deal with outliers. In this work, we propose two robust combining methods based on the AFTER algorithm (Yang, 2004a). Our approach utilizes robust loss functions in order to reduce the influence of outliers. Oracle inequalities for certain versions of these methods are obtained, which show that the combined forecasts automatically perform as well as the best individual among the pool of original forecasts. Systematic simulations and data examples show that the robust methods outperform the AFTER algorithm when outliers are likely to occur and perform on par with AFTER when there are no outliers. Comparison of the robust AFTERs with some commonly used combining methods also shows their potential advantages.