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Exponential Smoothing as a Special Case of a Linear Stochastic System

Author

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  • S. M. Pandit

    (University of Wisconsin, Madison, Wisconsin)

  • S. M. Wu

    (University of Wisconsin, Madison, Wisconsin)

Abstract

This paper derives a uniformly-sampled-autoregressive-moving-average (USAM) model for a second-order linear stochastic system, shows that exponential smoothing is a limiting case of the USAM model, and discusses the optimal value of the exponential-smoothing parameter and its sensitivity to mean-squared error of prediction. The USAM model is interpreted as a first-order system with first-order feedback; its limiting behavior explains why many business, economic, and quality-control systems are predicted well by exponential smoothing. The results are illustrated by examples of real-life data from IBM stock prices, and quality-control measurements of an automatic screw-machine operation.

Suggested Citation

  • S. M. Pandit & S. M. Wu, 1974. "Exponential Smoothing as a Special Case of a Linear Stochastic System," Operations Research, INFORMS, vol. 22(4), pages 868-879, August.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:4:p:868-879
    DOI: 10.1287/opre.22.4.868
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    Cited by:

    1. Eren Bas & Erol Egrioglu & Ufuk Yolcu, 2021. "Bootstrapped Holt Method with Autoregressive Coefficients Based on Harmony Search Algorithm," Forecasting, MDPI, vol. 3(4), pages 1-11, November.
    2. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.

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