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Exponential Smoothing: A Prediction Error Decomposition Principle

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  • Ralph D. Snyder

Abstract

In the exponential smoothing approach to forecasting, restrictions are often imposed on the smoothing parameters which ensure that certain components are exponentially weighted averages. In this paper, a new general restriction is derived on the basis that the one-step ahead prediction error can be decomposed into permanent and transient components. It is found that this general restriction reduces to the common restrictions used for simple, trend and seasonal exponential smoothing. As such, the prediction error argument provides the rationale for these restrictions.

Suggested Citation

  • Ralph D. Snyder, 2004. "Exponential Smoothing: A Prediction Error Decomposition Principle," Monash Econometrics and Business Statistics Working Papers 15/04, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2004-15
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp15-04.pdf
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    References listed on IDEAS

    as
    1. Peter R. Winters, 1960. "Forecasting Sales by Exponentially Weighted Moving Averages," Management Science, INFORMS, vol. 6(3), pages 324-342, April.
    2. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
    3. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
    4. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, October.
    5. Snyder, Ralph D & Ord, J Keith & Koehler, Anne B, 2001. "Prediction Intervals for ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 217-225, April.
    6. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
    7. Rob J. Hyndman & Muhammad Akram & Blyth Archibald, 2003. "Invertibility Conditions for Exponential Smoothing Models," Monash Econometrics and Business Statistics Working Papers 3/03, Monash University, Department of Econometrics and Business Statistics.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    time series analysis; prediction; exponential smoothing; ARIMA models; state space models.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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