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An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion

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  • Marcelo Bourguignon

    (Universidade Federal Do Rio Grande Do Norte)

  • Christian H. Weiß

    (Helmut Schmidt University)

Abstract

We present a novel first-order nonnegative integer-valued autoregressive model for stationary count data processes with Bernoulli-geometric marginals based on a new type of generalized thinning operator. It can be used for modeling time series of counts with equidispersion, underdispersion and overdispersion. The main properties of the model are derived, such as probability generating function, moments, transition probabilities and zero probability. The maximum likelihood method is used for estimating the model parameters. The proposed model is fitted to time series of counts of iceberg orders and of cases of family violence illustrating its capabilities in challenging cases of overdispersed and equidispersed count data.

Suggested Citation

  • Marcelo Bourguignon & Christian H. Weiß, 2017. "An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 847-868, December.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0536-4
    DOI: 10.1007/s11749-017-0536-4
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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.
    2. Robert Jung & A. Tremayne, 2011. "Useful models for time series of counts or simply wrong ones?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(1), pages 59-91, March.
    3. Kazuki Aoyama & Kunio Shimizu & S. Ong, 2008. "A first–passage time random walk distribution with five transition probabilities: a generalization of the shifted inverse trinomial," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 1-20, March.
    4. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    5. 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.
    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.
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    Cited by:

    1. Marcelo Bourguignon & Rodrigo M. R. Medeiros, 2022. "A simple and useful regression model for fitting count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 790-827, September.
    2. Kai Yang & Yao Kang & Dehui Wang & Han Li & Yajing Diao, 2019. "Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 863-889, October.
    3. Emrah Altun & Naushad Mamode Khan, 2022. "Modelling with the Novel INAR(1)-PTE Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1735-1751, September.

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