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A negative binomial thinning‐based bivariate INAR(1) process

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  • Qingchun Zhang
  • Dehui Wang
  • Xiaodong Fan

Abstract

This article considers a bivariate INAR(1) process based on an extension of the negative binomial thinning operator by prespecifying the distribution of the innovations. The dependence is introduced through the innovation components. The existence, uniqueness, strict stationarity, ergodicity, and some probabilistic properties of the process are derived. The estimation methods of conditional least squares and conditional maximum likelihood are considered. Some numerical results of the estimates are presented by simulation study. An application to crime data set is provided.

Suggested Citation

  • Qingchun Zhang & Dehui Wang & Xiaodong Fan, 2020. "A negative binomial thinning‐based bivariate INAR(1) process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 517-537, November.
    • Handle: RePEc:bla:stanee:v:74:y:2020:i:4:p:517-537
    DOI: 10.1111/stan.12210
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    References listed on IDEAS

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    1. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    2. Predrag M. Popović & Miroslav M. Ristić & Aleksandar S. Nastić, 2016. "A geometric bivariate time series with different marginal parameters," Statistical Papers, Springer, vol. 57(3), pages 731-753, September.
    3. 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.
    4. Christian Gouriéroux & Yang Lu, 2019. "Negative Binomial Autoregressive Process with Stochastic Intensity," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(2), pages 225-247, March.
    5. Yuvraj Sunecher & Naushad Mamode Khan & Miroslav M. Ristić & Vandna Jowaheer, 2019. "BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 625-653, December.
    6. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
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