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The Forecast Combination Puzzle: A Simple Theoretical Explanation

Author

Listed:
  • Gerda Claeskens

    (KU Leuven, Belgium)

  • Jan Magnus

    (VU University Amsterdam, the Netherlands)

  • Andrey Vasnev

    (University of Sydney, Australia)

  • Wendun Wang

    (Erasmus University, Rotterdam, the Netherlands)

Abstract

This papers 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 an application in the context of model selection.

Suggested Citation

  • Gerda Claeskens & Jan Magnus & Andrey Vasnev & Wendun Wang, 2014. "The Forecast Combination Puzzle: A Simple Theoretical Explanation," Tinbergen Institute Discussion Papers 14-127/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20140127
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    References listed on IDEAS

    as
    1. Hsiao, Cheng & Wan, Shui Ki, 2014. "Is there an optimal forecast combination?," Journal of Econometrics, Elsevier, vol. 178(P2), pages 294-309.
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    3. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    4. Jan R. Magnus & Giuseppe De Luca, 2016. "Weighted-Average Least Squares (Wals): A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 30(1), pages 117-148, February.
    5. Graefe, Andreas & Armstrong, J. Scott & Jones, Randall J. & Cuzán, Alfred G., 2014. "Combining forecasts: An application to elections," International Journal of Forecasting, Elsevier, vol. 30(1), pages 43-54.
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    7. Kabaila, Paul, 1995. "The Effect of Model Selection on Confidence Regions and Prediction Regions," Econometric Theory, Cambridge University Press, vol. 11(3), pages 537-549, June.
    8. James H. Stock & Mark W. Watson, 2003. "How did leading indicator forecasts perform during the 2001 recession?," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 89(Sum), pages 71-90.
    9. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    10. 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.
    11. Jeremy Smith & Kenneth F. Wallis, 2009. "A Simple Explanation of the Forecast Combination Puzzle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 331-355, June.
    12. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
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    More about this item

    Keywords

    forecast combination; optimal weights; model selection;
    All these keywords.

    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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