Prediction Intervals for Exponential Smoothing State Space Models

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Prediction Intervals for Exponential Smoothing State Space Models

Author Info

Hyndman, R.J. ()
Koehler, A.B.
Ord, J.K.
Snyder, R.D.

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Abstract

The main objective of this paper is to provide analytical expression for forecast variances that can be used in prediction intervals for the exponential smoothing methods. These expressions are based on state space models with a single source of error that underlie the exponential smoothing methods. In cases where an ARIMA model also underlies an exponential smoothing method, there is an equivalent state space model with the same variance expression. We also discuss relationships between these new ideas and previous suggestions for finding forecast variances and prediction intervals for the exponential smoothing methods.

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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 11/2001.

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Length: 22 pages
Date of creation: Dec 2001
Date of revision:
Handle: RePEc:msh:ebswps:2001-11

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

This paper has been announced in the following NEP Reports:

NEP-ALL-2002-04-25 (All new papers)
NEP-ECM-2002-04-25 (Econometrics)
NEP-ETS-2002-04-25 (Econometric Time Series)

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.:

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:
- Koehler, Anne B. & Snyder, Ralph D. & Ord, J. Keith, 2001. "Forecasting models and prediction intervals for the multiplicative Holt-Winters method," International Journal of Forecasting, Elsevier, vol. 17(2), pages 269-286. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Other versions:
- Hyndman, R.J. & Koehler, A.B. & Snyder, R.D. & Grose, S., 2000. "A State Space Framework for Automatic Forecasting Using Exponential Smoothing Methods," Monash Econometrics and Business Statistics Working Papers 9/2000, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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.
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)

Full references

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.)

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)
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!]
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!]
J Keith Ord & Ralph D Snyder & Anne B Koehler & Rob J Hyndman & Mark Leeds, 2005. "Time Series Forecasting: The Case for the Single Source of Error State Space," Monash Econometrics and Business Statistics Working Papers 7/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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:
- Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June. [Downloadable!] (restricted)
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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