Numerous forecast combination schemes with distinct properties have been proposed. However, to the best of our knowledge, there has been little discussion in the literature of the minimization of forecast outliers when combining forecasts. It would appear to have gone unnoticed that robust combining, which often improves the predictive accuracy (under square or absolute error losses) when innovation errors have a tail that is heavier than a normal distribution, may have a higher frequency of prediction outliers. Given the importance of reducing outlier forecasts, it is desirable to seek new loss functions which can achieve both the usual accuracy and outlier-protection simultaneously. In this paper, we propose a synthetic loss function and apply it to a general adaptive combination scheme for the outlier-protective combination of forecasts. Both the theoretical and numerical results support the advantages of the new method in terms of providing combined forecasts with fewer large forecast errors and comparable overall performances.
Bibliographical noteFunding Information:
We sincerely thank the two reviewers and the AE for their very helpful comments and suggestions for improving our work. We also thank the Minnesota Supercomputing Institute for providing computing resources. This work is partially supported by National Science Foundation grant DMS-1106576 .
- Forecast combination
- Loss function
- Outlier protection