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A State Space Framework for Automatic Forecasting Using Exponential Smoothing Methods

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Author Info
Hyndman, R.J.
Koehler, A.B.
Snyder, R.D.
Grose, S.

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Abstract

We provide a new approach to automatic business forecasting based on an extended range of exponential smoothing methods. Each method in our taxonomy of exponential smoothing methods can be shown to be equivalent to the forecasts obtained from a state space model. This allows (1) the easy calculation of the likelihood, the AIC and other model selection criteria; (2) the computation of prediction intervals for each method; and (3) random simulation from the underlying state space model. We demonstrate the methods by applying them to the data from the M-competition on the M3-competition.

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File URL: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2000/wp9-00.pdf
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Publisher Info
Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 9/2000.

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Length: 20 pages
Date of creation: Aug 2000
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Handle: RePEc:msh:ebswps:2000-9

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Related research
Keywords: Automatic forecasting; exponential smoothing; prediction intervals; state space models.;

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Find related papers by JEL classification:
C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!]
    Other versions:
  2. 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.
  3. Armstrong, J. Scott & Collopy, Fred, 1992. "Error measures for generalizing about forecasting methods: Empirical comparisons," International Journal of Forecasting, Elsevier, vol. 8(1), pages 69-80, June. [Downloadable!] (restricted)
  4. Chatfield, Chris & Yar, Mohammed, 1991. "Prediction intervals for multiplicative Holt-Winters," International Journal of Forecasting, Elsevier, vol. 7(1), pages 31-37, May. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ralph D Snyder, 2005. "A Pedant's Approach to Exponential Smoothing," Monash Econometrics and Business Statistics Working Papers 5/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  2. Md B. Billah & R.J. Hyndman & A.B. Koehler, 2003. "Empirical Information Criteria for Time Series Forecasting Model Selection," Monash Econometrics and Business Statistics Working Papers 2/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  3. 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 11/2001, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  4. Rob J. Hyndman & Yeasmin Khandakar, 2007. "Automatic time series forecasting: the forecast package for R," Monash Econometrics and Business Statistics Working Papers 6/07, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  5. George Athanasopoulos & Rob J. Hyndman, 2006. "Modelling and forecasting Australian domestic tourism," Monash Econometrics and Business Statistics Working Papers 19/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  6. Rob Hyndman & Muhammad Akram & Blyth Archibald, 2008. "The admissible parameter space for exponential smoothing models," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(2), pages 407-426, June. [Downloadable!] (restricted)
  7. Ralph D. Snyder & Anne B. Koehler & Rob J. Hyndman & J. Keith Ord, 2002. "Exponential Smoothing for Inventory Control: Means and Variances of Lead-Time Demand," Monash Econometrics and Business Statistics Working Papers 3/02, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  8. Ralph D. Snyder & Anne B. Koehler, 2008. "A View of Damped Trend as Incorporating a Tracking Signal into a State Space Model," Monash Econometrics and Business Statistics Working Papers 7/08, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  9. Muhammad Akram & Rob J. Hyndman & J. Keith Ord, 2007. "Non-linear exponential smoothing and positive data," Monash Econometrics and Business Statistics Working Papers 14/07, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  10. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310, October. [Downloadable!]
    Other versions:
  11. Rob J Hyndman & Muhammad Akram, 2006. "Some Nonlinear Exponential Smoothing Models are Unstable," Monash Econometrics and Business Statistics Working Papers 3/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  12. Ashton de Silva & Rob J. Hyndman & Ralph D. Snyder, 2007. "The vector innovation structural time series framework: a simple approach to multivariate forecasting," Monash Econometrics and Business Statistics Working Papers 3/07, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  13. Rob J Hyndman & Maxwell L. King & Ivet Pitrun & Baki Billah, 2002. "Local Linear Forecasts Using Cubic Smoothing Splines," Monash Econometrics and Business Statistics Working Papers 10/02, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  14. 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. [Downloadable!]
  15. George Athanasopoulos & Rob J Hyndman & Haiyan Song & Doris C Wu, 2008. "The tourism forecasting competition," Monash Econometrics and Business Statistics Working Papers 10/08, Monash University, Department of Econometrics and Business Statistics, revised Oct 2009. [Downloadable!]
  16. Rob J. Hyndman & Md. Shahid Ullah, 2005. "Robust forecasting of mortality and fertility rates: a functional data approach," Monash Econometrics and Business Statistics Working Papers 2/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  17. Hyndman, R.J. & Billah, B., 2001. "Unmasking the Theta Method," Monash Econometrics and Business Statistics Working Papers 5/2001, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  18. Rob J Hyndman & Heather Booth, 2006. "Stochastic population forecasts using functional data models for mortality, fertility and migration," Monash Econometrics and Business Statistics Working Papers 14/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  19. Rob J. Hyndman & Anne B. Koehler, 2005. "Another Look at Measures of Forecast Accuracy," Monash Econometrics and Business Statistics Working Papers 13/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  20. 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. [Downloadable!]
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