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Combining Forecasts: Operational Adjustments to Theoretically Optimal Rules


  • David C. Schmittlein

    (The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Jinho Kim

    (Korea Air Force Academy, Department of Management and Economics, Sangsuri Namilmyon Chungwongun, Chungbuk 363-849, Korea)

  • Donald G. Morrison

    (Anderson Graduate School of Management, University of California, Los Angeles, California 90024-1481)


Clemen and Winkler (1985) have described the theoretical effectiveness of Winkler's (1981) formula for optimally combining forecasts. The optimality of Winkler's formula is, however, contingent on actually knowing the forecasters' statistical properties, i.e., the variances and covariances of their forecasts. In realistic applications, of course, these properties have to be estimated, usually from a set of prior forecasts. In this case we show how the "operationally optimal" combining strategy differs from Winkler's "theoretically optimal" formula. Specifically, we provide figures indicating the operationally optimal strategy for combining two forecasts. We then propose a heuristic to choose the best set of parameter estimates in combining any number of forecasters and demonstrate its effectiveness via simulation.

Suggested Citation

  • David C. Schmittlein & Jinho Kim & Donald G. Morrison, 1990. "Combining Forecasts: Operational Adjustments to Theoretically Optimal Rules," Management Science, INFORMS, vol. 36(9), pages 1044-1056, September.
  • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:9:p:1044-1056

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    Cited by:

    1. Kamstra, Mark & Kennedy, Peter, 1998. "Combining qualitative forecasts using logit," International Journal of Forecasting, Elsevier, vol. 14(1), pages 83-93, March.
    2. 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.
    3. P. J. Lamberson & Scott E. Page, 2012. "Optimal Forecasting Groups," Management Science, INFORMS, vol. 58(4), pages 805-810, April.
    4. de Menezes, Lilian M. & W. Bunn, Derek & Taylor, James W., 2000. "Review of guidelines for the use of combined forecasts," European Journal of Operational Research, Elsevier, vol. 120(1), pages 190-204, January.
    5. Lessmann, Stefan & Sung, Ming-Chien & Johnson, Johnnie E.V. & Ma, Tiejun, 2012. "A new methodology for generating and combining statistical forecasting models to enhance competitive event prediction," European Journal of Operational Research, Elsevier, vol. 218(1), pages 163-174.
    6. Armstrong, J. Scott & Morwitz, Vicki G. & Kumar, V., 2000. "Sales Forecasts for Existing Consumer Products and Services: Do Purchase Intentions Contribute to Accuracy?," MPRA Paper 81689, University Library of Munich, Germany.
    7. Armstrong, J. Scott & Morwitz, Vicki G. & Kumar, V., 2000. "Sales forecasts for existing consumer products and services: Do purchase intentions contribute to accuracy?," International Journal of Forecasting, Elsevier, vol. 16(3), pages 383-397.
    8. Blattenberger, Gail & Fowles, Richard, 1995. "Road closure to mitigate avalanche danger: a case study for Little Cottonwood Canyon," International Journal of Forecasting, Elsevier, vol. 11(1), pages 159-174, March.


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