The forecast combination puzzle: A simple theoretical explanation

Gerda Claeskens, Jan R. Magnus, Andrey L. Vasnev, Wendun Wang

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

This paper offers a theoretical explanation for the stylized fact that forecast combinations with estimated optimal weights often perform poorly in applications. The properties of the forecast combination are typically derived under the assumption that the weights are fixed, while in practice they need to be estimated. If the fact that the weights are random rather than fixed is taken into account during the optimality derivation, then the forecast combination will be biased (even when the original forecasts are unbiased), and its variance will be larger than in the fixed-weight case. In particular, there is no guarantee that the 'optimal' forecast combination will be better than the equal-weight case, or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration.

Original languageEnglish
Pages (from-to)754-762
Number of pages9
JournalInternational Journal of Forecasting
Volume32
Issue number3
DOIs
Publication statusPublished - 2016

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Forecast combination
Optimality
Guarantee
Stylized facts

Keywords

  • Forecast combination
  • Optimal weights

Cite this

Claeskens, Gerda ; Magnus, Jan R. ; Vasnev, Andrey L. ; Wang, Wendun. / The forecast combination puzzle : A simple theoretical explanation. In: International Journal of Forecasting. 2016 ; Vol. 32, No. 3. pp. 754-762.
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The forecast combination puzzle : A simple theoretical explanation. / Claeskens, Gerda; Magnus, Jan R.; Vasnev, Andrey L.; Wang, Wendun.

In: International Journal of Forecasting, Vol. 32, No. 3, 2016, p. 754-762.

Research output: Contribution to JournalArticleAcademicpeer-review

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AB - This paper offers a theoretical explanation for the stylized fact that forecast combinations with estimated optimal weights often perform poorly in applications. The properties of the forecast combination are typically derived under the assumption that the weights are fixed, while in practice they need to be estimated. If the fact that the weights are random rather than fixed is taken into account during the optimality derivation, then the forecast combination will be biased (even when the original forecasts are unbiased), and its variance will be larger than in the fixed-weight case. In particular, there is no guarantee that the 'optimal' forecast combination will be better than the equal-weight case, or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration.

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