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A first order binomial mixed poisson integer-valued autoregressive model with serially dependent innovations

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  • Chen, Zezhun Chen
  • Dassios, Angelos
  • Tzougas, George

Abstract

Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of the mixed Poisson component, the model includes a large class of INAR(1) processes with different transition probabilities. Moreover, it can capture some overdispersion features coming from the data while keeping the innovations serially dependent. We discuss its statistical properties, stationarity conditions and transition probabilities for different mixing densities (Exponential, Lindley). Then, we derive the maximum likelihood estimation method and its asymptotic properties for this model. Finally, we demonstrate our approach using a real data example of iceberg count data from a financial system.

Suggested Citation

  • Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2023. "A first order binomial mixed poisson integer-valued autoregressive model with serially dependent innovations," LSE Research Online Documents on Economics 112222, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:112222
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    References listed on IDEAS

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    1. 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.
    2. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    3. Frey, Stefan & Sandås, Patrik, 2009. "The impact of iceberg orders in limit order books," CFR Working Papers 09-06, University of Cologne, Centre for Financial Research (CFR).
    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. Marcelo Bourguignon & Josemar Rodrigues & Manoel Santos-Neto, 2019. "Extended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(1), pages 101-118, January.
    6. Ruijun Bu & Brendan McCabe & Kaddour Hadri, 2008. "Maximum likelihood estimation of higher‐order integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 973-994, November.
    7. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    8. Kirchner, Matthias, 2016. "Hawkes and INAR(∞) processes," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2494-2525.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    count data time series; binomial-mixed Poisson INAR(1) models; mixed Poisson distribution; overdispersion; maximum likelihood estimation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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