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An Assessment of Alternative State Space Models for Count Time Series

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Author Info
Ralph D. Snyder ()
Gael M. Martin ()
Phillip Gould
Paul D. Feigin

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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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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
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Handle: RePEc:msh:ebswps:2007-4

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

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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    Other versions:
  5. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April. [Downloadable!] (restricted)
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  7. B.P.M. McCabe & G.M. Martin & R.K. Freeland, 2004. "Testing for Dependence in Non-Gaussian Time Series Data," Monash Econometrics and Business Statistics Working Papers 13/04, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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  8. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Blackwell Publishing, vol. 25(5), pages 701-722, 09. [Downloadable!] (restricted)
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  14. Strickland, Chris M. & Forbes, Catherine S. & Martin, Gael M., 2006. "Bayesian analysis of the stochastic conditional duration model," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2247-2267, May. [Downloadable!] (restricted)
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  15. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330. [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 & 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. [Downloadable!]
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