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An Assessment of Alternative State Space Models for Count Time Series

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  • Ralph D. Snyder

    ()

  • Gael M. Martin

    ()

  • Phillip Gould
  • Paul D. Feigin

Abstract

This paper compares two alternative models for autocorrelated count time series. The first model can be viewed as a 'single source of error' discrete state space model, in which a time-varying parameter is specified as a function of lagged counts, with no additional source of error introduced. The second model is the more conventional 'dual source of error' discrete state space model, in which the time-varying parameter is driven by a random autocorrelated process. Using the nomenclature of the literature, the two representations can be viewed as observation-driven and parameter-driven respectively, with the distinction between the two models mimicking that between analogous models for other non-Gaussian data such as financial returns and trade durations. The paper demonstrates that when adopting a conditional Poisson specification, the two models have vastly different dispersion/correlation properties, with the dual source model having properties that are a much closer match to the empirical properties of observed count series than are those of the single source model. Simulation experiments are used to measure the finite sample performance of maximum likelihood (ML) estimators of the parameters of each model, and ML-based predictors, with ML estimation implemented for the dual source model via a deterministic hidden Markov chain approach. Most notably, the numerical results indicate that despite the very different properties of the two models, predictive accuracy is reasonably robust to misspecification of the state space form.

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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 4/07.

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Length: 28 pages
Date of creation: May 2007
Date of revision:
Handle: RePEc:msh:ebswps:2007-4

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Keywords: Discrete state-space model; single source of error model; hidden Markov;

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References

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  1. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
  1. Ralph D. Snyder & Adrian Beaumont, 2007. "A Comparison of Methods for Forecasting Demand for Slow Moving Car Parts," Monash Econometrics and Business Statistics Working Papers 15/07, Monash University, Department of Econometrics and Business Statistics.

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