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The forecast combination puzzle: a simple theoretical explanation

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  • Gerda Claeskens
  • Jan Magnus
  • Andrey Vasnev
  • Wendun Wang

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 is larger than in the fixed-weights case. In particular, there is no guarantee that the 'optimal' forecast combination will be better than the equal-weights case or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration.

Suggested Citation

  • Gerda Claeskens & Jan Magnus & Andrey Vasnev & Wendun Wang, 2016. "The forecast combination puzzle: a simple theoretical explanation," Working Papers of Department of Decision Sciences and Information Management, Leuven 532152, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
    • Handle: RePEc:ete:kbiper:532152
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    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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