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Generalized Poisson autoregressive models for time series of counts

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  • Chen, Cathy W.S.
  • Lee, Sangyeol

Abstract

To better describe the characteristics of time series of counts such as over-dispersion, asymmetry, structural change, and a large proportion of zeros, this paper considers a class of generalized Poisson autoregressive models that properly capture flexible asymmetric and nonlinear responses through a switching mechanism. We also investigate zero-inflated generalized Poisson autoregressive models with a structural break that can cope with data having a large portion of zeros and changes in dynamics. We employ an adaptive Markov Chain Monte Carlo (MCMC) sampling scheme to locate the structural break and to estimate model parameters. As an illustration, we conduct a simulation study and empirical analysis of New South Wales crime data sets. Our findings show a remarkable improvement by modeling the data based on such generalized Poisson autoregressive models and the Bayesian method.

Suggested Citation

  • Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:51-67
    DOI: 10.1016/j.csda.2016.01.009
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    Cited by:

    1. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    2. Cem Cakmakli & Yasin Simsek, 2023. "Bridging the Covid-19 Data and the Epidemiological Model using Time-Varying Parameter SIRD Model," Papers 2301.13692, arXiv.org.
    3. Cathy W. S. Chen & Sangyeol Lee & K. Khamthong, 2021. "Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts," Computational Statistics, Springer, vol. 36(1), pages 261-281, March.
    4. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    5. Cem Cakmakli & Yasin Simsek, 2020. "Bridging the COVID-19 Data and the Epidemiological Model using Time Varying Parameter SIRD Model," Papers 2007.02726, arXiv.org, revised Feb 2021.
    6. Luis E. Nieto-Barajas, 2022. "Dependence on a collection of Poisson random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 21-39, March.
    7. Qi Li & Fukang Zhu, 2020. "Mean targeting estimator for the integer-valued GARCH(1, 1) model," Statistical Papers, Springer, vol. 61(2), pages 659-679, April.
    8. Chen, Cathy W.S. & Liu, Feng-Chi & Pingal, Aljo Clair, 2023. "Integer-valued transfer function models for counts that show zero inflation," Statistics & Probability Letters, Elsevier, vol. 193(C).
    9. Chen, Cathy W.S. & Chen, Chun-Shu & Hsiung, Mo-Hua, 2023. "Bayesian modeling of spatial integer-valued time series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    10. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    11. Bu Hyoung Lee, 2022. "Bootstrap Prediction Intervals of Temporal Disaggregation," Stats, MDPI, vol. 5(1), pages 1-13, February.
    12. Marinho G. Andrade & Katiane S. Conceição & Nalini Ravishanker, 2024. "Zero-modified count time series modeling with an application to influenza cases," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 611-637, September.
    13. Federico Bassetti & Giulia Carallo & Roberto Casarin, 2022. "First-order integer-valued autoregressive processes with Generalized Katz innovations," Papers 2202.02029, arXiv.org.
    14. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.

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