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Sensitivity of Weights in Combining Forecasts

Author

Listed:
  • Robert L. Winkler

    (Duke University, Durham, North Carolina)

  • Robert T. Clemen

    (University of Oregon, Eugene, Oregon)

Abstract

In the combination of forecasts, weighted averages that attempt to take into account the accuracy of the forecasts and any dependence among forecasts tend to perform poorly in practice. An important factor influencing this performance is the sensitivity, or instability, of the estimated weights used to generate the combined forecast. The intent of this paper is to look at this instability via graphs and the sampling distribution of the weights. Results are developed for the combination of two forecasts and extended to the m -forecast case by viewing the m -forecast case as a sequence of two-forecast combinations.

Suggested Citation

  • Robert L. Winkler & Robert T. Clemen, 1992. "Sensitivity of Weights in Combining Forecasts," Operations Research, INFORMS, vol. 40(3), pages 609-614, June.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:3:p:609-614
    DOI: 10.1287/opre.40.3.609
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    Cited by:

    1. Anil Gaba & Dana G. Popescu & Zhi Chen, 2019. "Assessing Uncertainty from Point Forecasts," Management Science, INFORMS, vol. 65(1), pages 90-106, January.
    2. Kourentzes, Nikolaos & Athanasopoulos, George, 2019. "Cross-temporal coherent forecasts for Australian tourism," Annals of Tourism Research, Elsevier, vol. 75(C), pages 393-409.
    3. Kornbluth, J. S. H., 1997. "Identifying feasible orderings for performance appraisal," Omega, Elsevier, vol. 25(3), pages 329-334, June.
    4. Pennings, Clint L.P. & van Dalen, Jan & Rook, Laurens, 2019. "Coordinating judgmental forecasting: Coping with intentional biases," Omega, Elsevier, vol. 87(C), pages 46-56.
    5. Weyant John, 2014. "Integrated assessment of climate change: state of the literature," Journal of Benefit-Cost Analysis, De Gruyter, vol. 5(3), pages 377-409, December.
    6. Chan, Felix & Pauwels, Laurent, 2019. "Equivalence of optimal forecast combinations under affine constraints," Working Papers BAWP-2019-02, University of Sydney Business School, Discipline of Business Analytics.
    7. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251, April.
    8. Robert T. Clemen & Robert L. Winkler, 1999. "Combining Probability Distributions From Experts in Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 19(2), pages 187-203, April.
    9. Mostaghimi, Mehdi, 1996. "Combining ranked mean value forecasts," European Journal of Operational Research, Elsevier, vol. 94(3), pages 505-516, November.
    10. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Petropoulos, Fotios, 2017. "Forecasting with temporal hierarchies," European Journal of Operational Research, Elsevier, vol. 262(1), pages 60-74.
    11. Leprince, Julien & Madsen, Henrik & Møller, Jan Kloppenborg & Zeiler, Wim, 2023. "Hierarchical learning, forecasting coherent spatio-temporal individual and aggregated building loads," Applied Energy, Elsevier, vol. 348(C).
    12. Radchenko, Peter & Vasnev, Andrey L. & Wang, Wendun, 2023. "Too similar to combine? On negative weights in forecast combination," International Journal of Forecasting, Elsevier, vol. 39(1), pages 18-38.
    13. Robert L. Winkler & Yael Grushka-Cockayne & Kenneth C. Lichtendahl Jr. & Victor Richmond R. Jose, 2019. "Probability Forecasts and Their Combination: A Research Perspective," Decision Analysis, INFORMS, vol. 16(4), pages 239-260, December.
    14. Jose, Victor Richmond R. & Winkler, Robert L., 2008. "Simple robust averages of forecasts: Some empirical results," International Journal of Forecasting, Elsevier, vol. 24(1), pages 163-169.
    15. Guanchun Wang & Sanjeev R. Kulkarni & H. Vincent Poor & Daniel N. Osherson, 2011. "Aggregating Large Sets of Probabilistic Forecasts by Weighted Coherent Adjustment," Decision Analysis, INFORMS, vol. 8(2), pages 128-144, June.
    16. Blanc, Sebastian M. & Setzer, Thomas, 2016. "When to choose the simple average in forecast combination," Journal of Business Research, Elsevier, vol. 69(10), pages 3951-3962.
    17. Taylor, James W. & Bunn, Derek W., 1999. "Investigating improvements in the accuracy of prediction intervals for combinations of forecasts: A simulation study," International Journal of Forecasting, Elsevier, vol. 15(3), pages 325-339, July.
    18. Barrow, Devon K. & Crone, Sven F., 2016. "A comparison of AdaBoost algorithms for time series forecast combination," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1103-1119.
    19. Robert L. Winkler*, 2015. "Equal Versus Differential Weighting in Combining Forecasts," Risk Analysis, John Wiley & Sons, vol. 35(1), pages 16-18, January.
    20. Astafyeva, Ekaterina & Turuntseva, Marina, 2024. "Forecast evaluation improving using the simplest methods of individual forecasts’ combination," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 74, pages 78-103.
    21. Emilian Dobrescu, 2014. "A Hybrid Forecasting Approach," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 16(35), pages 390-390, February.
    22. Tavana, M. & Kennedy, D. T. & Joglekar, P., 1996. "A group decision support framework for consensus ranking of technical manager candidates," Omega, Elsevier, vol. 24(5), pages 523-538, October.
    23. Paola Monari & Patrizia Agati, 2001. "Fiducial inference in combining expert judgements," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 81-97, January.
    24. Magnus, Jan R. & Vasnev, Andrey L., 2015. "Interpretation and use of sensitivity in econometrics, illustrated with forecast combinations," International Journal of Forecasting, Elsevier, vol. 31(3), pages 769-781.
    25. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251.

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    Keywords

    forecasting: combining forecasts;

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