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An integer-valued threshold autoregressive process based on negative binomial thinning

Author

Listed:
  • Kai Yang

    (Institute of Mathematics Jilin University)

  • Dehui Wang

    (Institute of Mathematics Jilin University)

  • Boting Jia

    (School of Statistics Jilin University of Finance and Economics)

  • Han Li

    (Institute of Mathematics Jilin University)

Abstract

In this paper, we introduce an integer-valued threshold autoregressive process, which is driven by independent negative-binomial distributed random variables and based on negative binomial thinning. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators and corresponding iterative algorithms are investigated for both the cases that the threshold variable is known or not. Also, the asymptotic properties of the estimators are obtained. Finally, some numerical results of the estimates and a real data example are presented.

Suggested Citation

  • Kai Yang & Dehui Wang & Boting Jia & Han Li, 2018. "An integer-valued threshold autoregressive process based on negative binomial thinning," Statistical Papers, Springer, vol. 59(3), pages 1131-1160, September.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0808-1
    DOI: 10.1007/s00362-016-0808-1
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    References listed on IDEAS

    as
    1. Hee-Young Kim & Yousung Park, 2008. "A non-stationary integer-valued autoregressive model," Statistical Papers, Springer, vol. 49(3), pages 485-502, July.
    2. 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.
    3. 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.
    4. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    5. Andreia Hall & Manuel Scotto & João Cruz, 2010. "Extremes of integer-valued moving average sequences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 359-374, August.
    6. 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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    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. Han Li & Zijian Liu & Kai Yang & Xiaogang Dong & Wenshan Wang, 2024. "A pth-order random coefficients mixed binomial autoregressive process with explanatory variables," Computational Statistics, Springer, vol. 39(5), pages 2581-2604, July.
    3. Yixuan Fan & Jianhua Cheng & Dehui Wang, 2024. "A new integer-valued threshold autoregressive process based on modified negative binomial operator driven by explanatory variables," Statistical Papers, Springer, vol. 65(9), pages 5873-5901, December.
    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.

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