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Invertibility Conditions for Exponential Smoothing Models

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Author Info

  • Rob J. Hyndman

    ()

  • Muhammad Akram
  • Blyth Archibald

Abstract

In this article we discuss invertibility conditions for some state space models, including the models that underly simple exponential smoothing, Holt's linear method, Holt-Winters' additive method and damped trend versions of Holt's and Holt-Winters' methods. The parameter space for which the model is invertible is compared to the usual parameter regions. We find that the usual parameter restrictions (requiring all smoothing parameters to lie between 0 and 1) do not always lead to invertible models. Conversely, some invertible models have parameters which lie outside the usual region. We also find that all seasonal exponential smoothing methods are non-invertible when the usual equations are used. However, this does not affect the forecast mean. Alternative models are presented which solve the problem while retaining the basic exponential smoothing ideas.

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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 3/03.

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Length: 19 pages
Date of creation: Apr 2003
Date of revision:
Handle: RePEc:msh:ebswps:2003-3

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Related research

Keywords: exponential smoothing; invertibility; state space models.;

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Cited by:
  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.
  2. 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.

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