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A new Bayesian formulation for Holt's exponential smoothing

Author

Listed:
  • Robert R. Andrawis

    (Data Mining Center of Excellence, MCIT, Cairo, Egypt)

  • Amir F. Atiya

    (Department of Computer Engineering, Cairo University, Giza, Egypt)

Abstract

In this paper we propose a Bayesian forecasting approach for Holt's additive exponential smoothing method. Starting from the state space formulation, a formula for the forecast is derived and reduced to a two-dimensional integration that can be computed numerically in a straightforward way. In contrast to much of the work for exponential smoothing, this method produces the forecast density and, in addition, it considers the initial level and initial trend as part of the parameters to be evaluated. Another contribution of this paper is that we have derived a way to reduce the computation of the maximum likelihood parameter estimation procedure to that of evaluating a two-dimensional grid, rather than applying a five-variable optimization procedure. Simulation experiments confirm that both proposed methods give favorable performance compared to other approaches. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Robert R. Andrawis & Amir F. Atiya, 2009. "A new Bayesian formulation for Holt's exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 218-234.
    • Handle: RePEc:jof:jforec:v:28:y:2009:i:3:p:218-234
    DOI: 10.1002/for.1094
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    References listed on IDEAS

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    1. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    2. Hyndman, R.J. & Koehler, A.B. & Ord, J.K. & Snyder, R.D., 2001. "Prediction Intervals for Exponential Smoothing State Space Models," Monash Econometrics and Business Statistics Working Papers 11/01, Monash University, Department of Econometrics and Business Statistics.
    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.
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    5. Makridakis, Spyros & Hibon, Michele, 1991. "Exponential smoothing: The effect of initial values and loss functions on post-sample forecasting accuracy," International Journal of Forecasting, Elsevier, vol. 7(3), pages 317-330, November.
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    7. Laurence Broze & Guy Melard, 1990. "Exponential smoothing: estimation by maximum likelihood," ULB Institutional Repository 2013/13716, ULB -- Universite Libre de Bruxelles.
    8. Koning, Alex J. & Franses, Philip Hans & Hibon, Michele & Stekler, H.O., 2005. "The M3 competition: Statistical tests of the results," International Journal of Forecasting, Elsevier, vol. 21(3), pages 397-409.
    9. 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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    Cited by:

    1. Alysha M De Livera, 2010. "Automatic forecasting with a modified exponential smoothing state space framework," Monash Econometrics and Business Statistics Working Papers 10/10, Monash University, Department of Econometrics and Business Statistics.
    2. Andrawis, Robert R. & Atiya, Amir F. & El-Shishiny, Hisham, 2011. "Combination of long term and short term forecasts, with application to tourism demand forecasting," International Journal of Forecasting, Elsevier, vol. 27(3), pages 870-886, July.
    3. Andrawis, Robert R. & Atiya, Amir F. & El-Shishiny, Hisham, 2011. "Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition," International Journal of Forecasting, Elsevier, vol. 27(3), pages 672-688, July.
    4. Mirko Kremer & Brent Moritz & Enno Siemsen, 2011. "Demand Forecasting Behavior: System Neglect and Change Detection," Management Science, INFORMS, vol. 57(10), pages 1827-1843, October.

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