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Some theoretical results on forecast combinations

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  • Chan, Felix
  • Pauwels, Laurent L.

Abstract

This paper proposes a framework for the analysis of the theoretical properties of forecast combination, with the forecast performance being measured in terms of mean squared forecast errors (MSFE). Such a framework is useful for deriving all existing results with ease. In addition, it also provides insights into two forecast combination puzzles. Specifically, it investigates why a simple average of forecasts often outperforms forecasts from single models in terms of MSFEs, and why a more complicated weighting scheme does not always perform better than a simple average. In addition, this paper presents two new findings that are particularly relevant in practice. First, the MSFE of a forecast combination decreases as the number of models increases. Second, the conventional approach to the selection of optimal models, based on a simple comparison of MSFEs without further statistical testing, leads to a biased selection.

Suggested Citation

  • Chan, Felix & Pauwels, Laurent L., 2018. "Some theoretical results on forecast combinations," International Journal of Forecasting, Elsevier, vol. 34(1), pages 64-74.
  • Handle: RePEc:eee:intfor:v:34:y:2018:i:1:p:64-74
    DOI: 10.1016/j.ijforecast.2017.08.005
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    References listed on IDEAS

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    3. Pauwels, Laurent & Radchenko, Peter & Vasnev, Andrey, 2019. "Higher Moment Constraints for Predictive Density Combinations," Working Papers BAWP-2019-01, University of Sydney Business School, Discipline of Business Analytics.
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    13. Post, Thierry & Karabatı, Selçuk & Arvanitis, Stelios, 2019. "Robust optimization of forecast combinations," International Journal of Forecasting, Elsevier, vol. 35(3), pages 910-926.
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    15. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2020. "The M4 Competition: 100,000 time series and 61 forecasting methods," International Journal of Forecasting, Elsevier, vol. 36(1), pages 54-74.
    16. Zhentao Shi & Liangjun Su & Tian Xie, 2020. "L2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis," Papers 2010.09477, arXiv.org, revised Aug 2022.
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    18. Kourentzes, Nikolaos & Barrow, Devon & Petropoulos, Fotios, 2019. "Another look at forecast selection and combination: Evidence from forecast pooling," International Journal of Production Economics, Elsevier, vol. 209(C), pages 226-235.
    19. Eraslan, Sercan & Nöller, Marvin, 2020. "Recession probabilities falling from the STARs," Discussion Papers 08/2020, Deutsche Bundesbank.
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    21. Spiliotis, Evangelos & Nikolopoulos, Konstantinos & Assimakopoulos, Vassilios, 2019. "Tales from tails: On the empirical distributions of forecasting errors and their implication to risk," International Journal of Forecasting, Elsevier, vol. 35(2), pages 687-698.

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