An Assessment of Alternative State Space Models for Count Time Series
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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- J. Durbin & S. J. Koopman, 2000.
"Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives,"
Journal of the Royal Statistical Society Series B,
Royal Statistical Society, vol. 62(1), pages 3-56.
- Durbin, J. & Koopman, S.J.M., 1998. "Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives," Discussion Paper 1998-142, Tilburg University, Center for Economic Research.
- Chris M. Strickland & Catherine S. Forbes & Gael M. Martin, 2003.
"Bayesian Analysis of the Stochastic Conditional Duration Model,"
Monash Econometrics and Business Statistics Working Papers
14/03, Monash University, Department of Econometrics and Business Statistics.
- 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.
- Heinen, Andreas, 2003.
"Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model,"
8113, University Library of Munich, Germany.
- HEINEN, AndrÃ©as, 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).
- Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998.
"Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 65(3), pages 361-93, July.
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
- Tom Doan, . "KSCPOSTDRAW: RATS procedure to draw from posterior density needed in stochastic volatility model," Statistical Software Components RTS00101, Boston College Department of Economics.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
- Tom Doan, . "RATS programs to replicate Jacquier, Polson, Rossi (1994) stochastic volatility," Statistical Software Components RTZ00105, Boston College Department of Economics.
- 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.
- Keith Freeland & Brendan McCabe & Gael Martin, 2004. "Testing for Dependence in Non-Gaussian Time Series Data," Econometric Society 2004 Australasian Meetings 313, Econometric Society.
- Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543.
- Tom Doan, . "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, 09.
- Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
- Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Sylvia Fr�Hwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, vol. 93(4), pages 827-841, December.
- Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
- 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.
- Rong Zhu & Harry Joe, 2006. "Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 725-738, 09.
- Jung, Robert & Kukuk, Martin & Liesenfeld, Roman, 2005. "Time Series of Count Data : Modelling and Estimation," Economics Working Papers 2005,08, Christian-Albrechts-University of Kiel, Department of Economics.
- 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.
- BAUWENS, Luc & VEREDAS, David, . "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," CORE Discussion Papers RP 1688, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Scott I. White & Adam E. Clements & Stan Hurn, 2004. "Discretised Non-Linear Filtering for Dynamic Latent Variable Models: with Application to Stochastic Volatility," Econometric Society 2004 Australasian Meetings 46, Econometric Society.
- 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.
- Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-17, October.
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