Combining forecasts for universally optimal performance

Wei Qian, Craig A. Rolling, Gang Cheng, Yuhong Yang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


There are two potential directions of forecast combination: combining for adaptation and combining for improvement. The former direction targets the performance of the best forecaster, while the latter attempts to combine forecasts to improve on the best forecaster. It is often useful to infer which goal is more appropriate so that a suitable combination method may be used. This paper proposes an AI-AFTER approach that can not only determine the appropriate goal of forecast combination but also intelligently combine the forecasts to automatically achieve the proper goal. As a result of this approach, the combined forecasts from AI-AFTER perform well universally in both adaptation and improvement scenarios. The proposed forecasting approach is implemented in our R package AIafter, which is available at

Original languageEnglish (US)
Pages (from-to)193-208
Number of pages16
JournalInternational Journal of Forecasting
Issue number1
StatePublished - Jan 1 2022

Bibliographical note

Funding Information:
Qian’s research is partially supported by U.S. NSF grant DMS-1916376 and JPMC Faculty Fellowship. We would like to thank the Editor, Associate Editor and two anonymous referees for their valuable comments that help to improve this manuscript significantly.

Publisher Copyright:
© 2021 International Institute of Forecasters


  • Combining forecasts
  • Model averaging
  • Regression
  • Statistical tests


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