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Exponential Smoothing: A Prediction Error Decomposition Principle

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  • Ralph D. Snyder

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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.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp15-04.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 15/04.

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Length: 10 pages
Date of creation: Aug 2004
Date of revision:
Handle: RePEc:msh:ebswps:2004-15

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Related research

Keywords: time series analysis; prediction; exponential smoothing; ARIMA models; state space models.;

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References

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  1. 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 9/00, Monash University, Department of Econometrics and Business Statistics.
  2. Snyder, R.D. & Ord, J.K. & Koehler, A.B., 1997. "Prediction Intervals for Arima Models," Monash Econometrics and Business Statistics Working Papers 8/97, Monash University, Department of Econometrics and Business Statistics.
  3. Peter R. Winters, 1960. "Forecasting Sales by Exponentially Weighted Moving Averages," Management Science, INFORMS, vol. 6(3), pages 324-342, April.
  4. Harvey, A.C. & Koopman, S.J.M., 1999. "Signal Extraction and the Formulation of Unobserved Components Models," Discussion Paper 1999-44, Tilburg University, Center for Economic Research.
  5. 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.
  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.
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