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Forecasting Models and Prediction Intervals for the Multiplicative Holt-Winters Method

Author

Listed:
  • Koehler, A.B.
  • Snyder, R.D.
  • Ord, J.K.

Abstract

A new class of models for data showing trend and multiplicative seasonality is presented. The models allow the forecast error variance to depend on the trend and/ or the seasonality. It can be shown that each of these models has the same updating equations and forecast functions as the multiplicative Holt-Winters method, regardless of whether the error variation in the model is constant or not. While the point forecasts from the different models are identical, the prediction intervals will, of course, depend on the structure of the error variance and so it is essential to be able to choose the most appropriate form of model. Two methods for making this choice are presented and examined by simulation.

Suggested Citation

  • Koehler, A.B. & Snyder, R.D. & Ord, J.K., 1999. "Forecasting Models and Prediction Intervals for the Multiplicative Holt-Winters Method," Monash Econometrics and Business Statistics Working Papers 1/99, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:1999-1
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/1999/wp1-99.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. Archibald, Blyth C., 1990. "Parameter space of the Holt-winters' model," International Journal of Forecasting, Elsevier, vol. 6(2), pages 199-209, July.
    3. Ahn, Sung K. & Reinsel, Gregory C., 1994. "Estimation of partially nonstationary vector autoregressive models with seasonal behavior," Journal of Econometrics, Elsevier, vol. 62(2), pages 317-350, June.
    4. 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.
    5. Chatfield, Chris & Yar, Mohammed, 1991. "Prediction intervals for multiplicative Holt-Winters," International Journal of Forecasting, Elsevier, vol. 7(1), pages 31-37, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Forecasting; Prediction Intervals; Multiplicative Holt-Winters;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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