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Mixed Poisson INAR(1) processes

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  • Wagner Barreto-Souza

    (Universidade Federal de Minas Gerais)

Abstract

Overdispersion is a phenomenon commonly observed in count time series. Since Poisson distribution is equidispersed, the INteger-valued AutoRegressive (INAR) process with Poisson marginals is not adequate for modelling overdispersed counts. To overcome this problem, in this paper we propose a general class of first-order INAR processes for modelling overdispersed count time series. The proposed INAR(1) processes have marginals belonging to a class of mixed Poisson distributions, which are overdispersed. With this, our class of overdispersed count models have the known negative binomial INAR(1) process as particular case and open the possibility of introducing new INAR(1) processes, such as the Poisson-inverse Gaussian INAR(1) model, which is discussed here with some details. We establish a condition to our class of overdispersed INAR processes is well-defined and study some statistical properties. We propose estimators for the parameters and establish their consistency and asymptotic normality. A small Monte Carlo simulation to evaluate the finite-sample performance of the proposed estimators is presented and one application to a real data set illustrates the usefulness of our proposed overdispersed count processes.

Suggested Citation

  • Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:6:d:10.1007_s00362-017-0912-x
    DOI: 10.1007/s00362-017-0912-x
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    References listed on IDEAS

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    1. 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 407-417, October.
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    4. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
    5. Simos Meintanis & Dimitris Karlis, 2014. "Validation tests for the innovation distribution in INAR time series models," Computational Statistics, Springer, vol. 29(5), pages 1221-1241, October.
    6. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    7. Mansour Aghababaei Jazi & Geoff Jones & Chin-Diew Lai, 2012. "First-order integer valued AR processes with zero inflated poisson innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(6), pages 954-963, November.
    8. Miroslav M. Ristić & Aleksandar S. Nastić & Ana V. Miletić Ilić, 2013. "A geometric time series model with dependent Bernoulli counting series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 466-476, July.
    9. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    10. Wagner Barreto-Souza & Marcelo Bourguignon, 2015. "A skew INAR(1) process on $${\mathbb {Z}}$$ Z," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 189-208, April.
    11. Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.
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    Cited by:

    1. Yuhyeong Jang & Raanju R. Sundararajan & Wagner Barreto-Souza & Elizabeth Wheaton-Paramo, 2024. "Determining economic factors for sex trafficking in the United States using count time series regression," Empirical Economics, Springer, vol. 67(1), pages 337-354, July.

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