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A seasonal geometric INAR process based on negative binomial thinning operator

Author

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  • Shengqi Tian

    (Jilin University)

  • Dehui Wang

    (Jilin University)

  • Shuai Cui

    (Jilin University)

Abstract

In this article, we propose a new seasonal geometric integer-valued autoregressive process based on the negative binomial thinning operator with seasonal period s. Some basic probabilistic and statistical properties of the model are discussed. Conditional maximum likelihood estimators are obtained, and the asymptotic properties of the estimators are established. Some theoretical results of point forecasts are obtained. Numerical results are presented. At the end, two real data examples are investigated to assess the performance of our new model.

Suggested Citation

  • Shengqi Tian & Dehui Wang & Shuai Cui, 2020. "A seasonal geometric INAR process based on negative binomial thinning operator," Statistical Papers, Springer, vol. 61(6), pages 2561-2581, December.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1060-7
    DOI: 10.1007/s00362-018-1060-7
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    References listed on IDEAS

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    1. A. Alzaid & M. Al‐Osh, 1988. "First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 42(1), pages 53-61, March.
    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. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    4. A. Alzaid & M. Al-Osh, 1993. "Some autoregressive moving average processes with generalized Poisson marginal distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 223-232, June.
    5. Aleksandar S. Nastić & Petra N. Laketa & Miroslav M. Ristić, 2016. "Random environment integer-valued autoregressive process," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 267-287, March.
    6. 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, September.
    7. 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, May.
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    Cited by:

    1. Shaomin Li & Haoyu Wei & Xiaoyu Lei, 2021. "Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations," Papers 2110.03552, arXiv.org, revised Feb 2022.
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