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First-order random coefficients integer-valued threshold autoregressive processes

Author

Listed:
  • Han Li

    (Jilin University)

  • Kai Yang

    (Jilin University)

  • Shishun Zhao

    (Jilin University)

  • Dehui Wang

    (Jilin University)

Abstract

In this paper, we introduce a first-order random coefficient integer-valued threshold autoregressive process, which is based on binomial thinning. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators are derived for both the cases that the threshold variable is known or not. The asymptotic properties of the estimators are established. Moreover, forecasting problem is addressed. Finally, some numerical results of the estimates and a real data example are presented.

Suggested Citation

  • Han Li & Kai Yang & Shishun Zhao & Dehui Wang, 2018. "First-order random coefficients integer-valued threshold autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 305-331, July.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:3:d:10.1007_s10182-017-0306-3
    DOI: 10.1007/s10182-017-0306-3
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    References listed on IDEAS

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    1. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
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    3. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
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    5. Chao Wang & Heng Liu & Jian-Feng Yao & Richard A. Davis & Wai Keung Li, 2014. "Self-Excited Threshold Poisson Autoregression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 777-787, June.
    6. Tobias A. Möller & Maria Eduarda Silva & Christian H. Weiß & Manuel G. Scotto & Isabel Pereira, 2016. "Self-exciting threshold binomial autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 369-400, October.
    7. Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
    8. 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.
    9. Robert Jung & Gerd Ronning & A. Tremayne, 2005. "Estimation in conditional first order autoregression with discrete support," Statistical Papers, Springer, vol. 46(2), pages 195-224, April.
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    Citations

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    Cited by:

    1. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    2. Kai Yang & Han Li & Dehui Wang & Chenhui Zhang, 2021. "Random coefficients integer-valued threshold autoregressive processes driven by logistic regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 533-557, December.
    3. 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.
    4. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    5. Yao Kang & Dehui Wang & Kai Yang, 2021. "A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion," Statistical Papers, Springer, vol. 62(2), pages 745-767, April.

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