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Some geometric mixed integer-valued autoregressive (INAR) models

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  • Nastić, Aleksandar S.
  • Ristić, Miroslav M.
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    Abstract

    In this paper, we introduce some mixed integer-valued autoregressive models of orders 1 and 2 with geometric marginal distributions, denoted by MGINAR(1) and MGINAR(2), using a mixture of the well-known binomial and the negative binomial thinning. The distributions of the innovation processes are derived and several properties of the model are discussed. Conditional least squares and Yule–Walker estimators are obtained, and some numerical results of the estimations are presented. A real-life data example is investigated to assess the performance of the models.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 4 ()
    Pages: 805-811

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:805-811

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    Related research

    Keywords: INAR(1) models; INAR(2) models; Binomial thinning; Negative binomial thinning; Geometric marginal distribution;

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    1. A. Alzaid & M. Al-Osh, 1993. "Some autoregressive moving average processes with generalized Poisson marginal distributions," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 45(2), pages 223-232, June.
    2. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer, Springer, vol. 92(3), pages 319-341, August.
    3. Haitao Zheng & Ishwar V. Basawa & Somnath Datta, 2006. "Inference for pth-order random coefficient integer-valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 411-440, 05.
    4. Rong Zhu & Harry Joe, 2006. "Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 725-738, 09.
    5. Weiß, Christian H., 2008. "The combined INAR(p) models for time series of counts," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(13), pages 1817-1822, September.
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