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Forecasting Applications of an Adaptive Multiple Exponential Smoothing Model


  • Phillip G. Enns

    (St. Louis University)

  • Joseph A. Machak

    (University of Michigan)

  • W. Allen Spivey

    (University of Michigan)

  • William J. Wrobleski

    (University of Michigan)


This paper introduces a class of multiple exponential smoothing models useful in automated or minimal intervention industrial forecasting systems. These models are an alternative to simple univariate exponential smoothing and Trigg and Leach type adaptive models, which treat time series as unrelated and so cannot explicitly accommodate interrelationships that may exist between two or more time series. Moreover, the multiple models are adaptive in that the smoothing matrix, which is a generalization of the smoothing constant of univariate models, changes from period to period. Maximum likelihood estimates of the model parameters, including the full variance-covariance structure as well as the smoothing matrix, are provided, thus freeing the model user from the need for making ad hoc estimates of parameter values, a feature of simple univariate exponential smoothing. The forecast performance of this multiple time series model is compared with that of other univariate models using automobile sales data and some promising results are obtained.

Suggested Citation

  • Phillip G. Enns & Joseph A. Machak & W. Allen Spivey & William J. Wrobleski, 1982. "Forecasting Applications of an Adaptive Multiple Exponential Smoothing Model," Management Science, INFORMS, vol. 28(9), pages 1035-1044, September.
  • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:9:p:1035-1044
    DOI: 10.1287/mnsc.28.9.1035

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    Cited by:

    1. George Athanasopoulos & Ashton de Silva, 2010. "Multivariate exponential smoothing for forecasting tourist arrivals to Australia and New Zealand," Monash Econometrics and Business Statistics Working Papers 11/09, Monash University, Department of Econometrics and Business Statistics.
    2. Corberán-Vallet, Ana & Bermúdez, José D. & Vercher, Enriqueta, 2011. "Forecasting correlated time series with exponential smoothing models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 252-265.
    3. Mirko Kremer & Enno Siemsen & Douglas J. Thomas, 2016. "The Sum and Its Parts: Judgmental Hierarchical Forecasting," Management Science, INFORMS, vol. 62(9), pages 2745-2764, September.
    4. Bermúdez, José D. & Corberán-Vallet, Ana & Vercher, Enriqueta, 2009. "Multivariate exponential smoothing: A Bayesian forecast approach based on simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1761-1769.
    5. Corberán-Vallet, Ana & Bermúdez, José D. & Vercher, Enriqueta, 2011. "Forecasting correlated time series with exponential smoothing models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 252-265, April.
    6. James W. Taylor, 2004. "Smooth transition exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 385-404.
    7. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
    8. Triantafyllopoulos, Kostas, 2006. "Multivariate discount weighted regression and local level models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3702-3720, August.

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    forecasting: time series;


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