An Assessment of Alternative State Space Models for Count Time Series

Ralph David Snyder (), Gael Margaret Martin, Phillip Gould and Paul D. Feigin

No 4/07, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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.

Keywords: Discrete state-space model; single source of error model; hidden Markov (search for similar items in EconPapers)
JEL-codes: C13 C22 C46 C53 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2007-05
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