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The forecast combination puzzle: A simple theoretical explanation

Author

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

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.

Suggested Citation

  • Claeskens, Gerda & Magnus, Jan R. & Vasnev, Andrey L. & Wang, Wendun, 2016. "The forecast combination puzzle: A simple theoretical explanation," International Journal of Forecasting, Elsevier, vol. 32(3), pages 754-762.
    • Handle: RePEc:eee:intfor:v:32:y:2016:i:3:p:754-762
    DOI: 10.1016/j.ijforecast.2015.12.005
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    References listed on IDEAS

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    1. Hsiao, Cheng & Wan, Shui Ki, 2014. "Is there an optimal forecast combination?," Journal of Econometrics, Elsevier, vol. 178(P2), pages 294-309.
    2. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, September.
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    7. Liang, Hua & Zou, Guohua & Wan, Alan T. K. & Zhang, Xinyu, 2011. "Optimal Weight Choice for Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1053-1066.
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    More about this item

    Keywords

    Forecast combination; Optimal weights;

    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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