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Self-exciting threshold binomial autoregressive processes

Author

Listed:
  • Tobias A. Möller

    (Helmut Schmidt University)

  • Maria Eduarda Silva

    (University of Porto)

  • Christian H. Weiß

    (Helmut Schmidt University)

  • Manuel G. Scotto

    (IST University of Lisbon)

  • Isabel Pereira

    (University of Aveiro)

Abstract

We introduce a new class of integer-valued self-exciting threshold models, which is based on the binomial autoregressive model of order one as introduced by McKenzie (Water Resour Bull 21:645–650, 1985. doi: 10.1111/j.1752-1688.1985.tb05379.x ). Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the performance of these models is illustrated through a simulation study and an empirical application to a set of measle cases in Germany.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:100:y:2016:i:4:d:10.1007_s10182-015-0264-6
    DOI: 10.1007/s10182-015-0264-6
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    References listed on IDEAS

    as
    1. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    2. Markku Lanne & Pentti Saikkonen, 2005. "Non-linear GARCH models for highly persistent volatility," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 251-276, July.
    3. Noelle I. Samia & Kung-Sik Chan & Nils Chr. Stenseth, 2007. "A generalized threshold mixed model for analyzing nonnormal nonlinear time series, with application to plague in Kazakhstan," Biometrika, Biometrika Trust, vol. 94(1), pages 101-118.
    4. Wai-Sum Chan & Albert Wong & Howell Tong, 2004. "Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 37-61.
    5. Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
    6. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive density and conditional confidence interval accuracy tests," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 187-228.
    7. 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.
    8. Christian H. Weiß & Philip K. Pollett, 2014. "Binomial Autoregressive Processes With Density-Dependent Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 115-132, March.
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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. 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.
    4. 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.
    5. Tobias A. Möller & Christian H. Weiß & Hee-Young Kim & Andrei Sirchenko, 2018. "Modeling Zero Inflation in Count Data Time Series with Bounded Support," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 589-609, June.
    6. Zhang, Rui, 2024. "Asymmetric beta-binomial GARCH models for time series with bounded support," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    7. Cláudia Santos & Isabel Pereira & Manuel G. Scotto, 2021. "On the theory of periodic multivariate INAR processes," Statistical Papers, Springer, vol. 62(3), pages 1291-1348, June.

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