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On MCMC sampling in self-exciting integer-valued threshold time series models

Author

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  • Yang, Kai
  • Yu, Xinyang
  • Zhang, Qingqing
  • Dong, Xiaogang

Abstract

Markov Chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches in statistics. However, due to the complex structure of the models, this method remains an open problem for threshold integer-valued time series models. This study develops Bayesian inference for a class of self-exciting integer-valued threshold autoregressive models, which is implemented by means of a new MCMC algorithm. By introducing the latent variables series, a complete data likelihood is obtained. Based on which, the full conditional distributions are easily obtained with familiar forms. Furthermore, by maximizing the complete data likelihood, the threshold parameter is also accurately estimated. Finally, the performance of the MCMC algorithm is evaluated via some simulations and a real data example.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:169:y:2022:i:c:s0167947321002449
    DOI: 10.1016/j.csda.2021.107410
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    References listed on IDEAS

    as
    1. 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.
    2. Kurt Brannas & A. M. M. Shahiduzzaman Quoreshi, 2010. "Integer-valued moving average modelling of the number of transactions in stocks," Applied Financial Economics, Taylor & Francis Journals, vol. 20(18), pages 1429-1440.
    3. Barnett, Glen & Kohn, Robert & Sheather, Simon, 1996. "Bayesian estimation of an autoregressive model using Markov chain Monte Carlo," Journal of Econometrics, Elsevier, vol. 74(2), pages 237-254, October.
    4. Akanksha S. Kashikar & Neelabh Rohan & T.V. Ramanathan, 2013. "Integer autoregressive models with structural breaks," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2653-2669, December.
    5. Agosto, Arianna & Cavaliere, Giuseppe & Kristensen, Dennis & Rahbek, Anders, 2016. "Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 640-663.
    6. 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.
    7. Bu, Ruijun & McCabe, Brendan, 2008. "Model selection, estimation and forecasting in INAR(p) models: A likelihood-based Markov Chain approach," International Journal of Forecasting, Elsevier, vol. 24(1), pages 151-162.
    8. Han Li & Kai Yang & Dehui Wang, 2017. "Quasi-likelihood inference for self-exciting threshold integer-valued autoregressive processes," Computational Statistics, Springer, vol. 32(4), pages 1597-1620, December.
    9. 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.
    10. Ausin, Maria Concepcion & Galeano, Pedro, 2007. "Bayesian estimation of the Gaussian mixture GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2636-2652, February.
    11. Han Li & Kai Yang & Dehui Wang, 2019. "A threshold stochastic volatility model with explanatory variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 73(1), pages 118-138, February.
    12. Feike C. Drost & Ramon van den Akker & Bas J. M. Werker, 2009. "Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR(p) models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 467-485, April.
    13. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Linde, 2014. "The deviance information criterion: 12 years on," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 485-493, June.
    14. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
    15. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    16. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    17. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    18. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    19. Peter Neal & T. Subba Rao, 2007. "MCMC for Integer‐Valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 92-110, January.
    20. 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.
    21. 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.
    22. R. Freeland, 2010. "True integer value time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 217-229, September.
    23. Richard A. Davis & Konstantinos Fokianos & Scott H. Holan & Harry Joe & James Livsey & Robert Lund & Vladas Pipiras & Nalini Ravishanker, 2021. "Count Time Series: A Methodological Review," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1533-1547, May.
    24. Li, Yong & Yu, Jun & Zeng, Tao, 2020. "Deviance information criterion for latent variable models and misspecified models," Journal of Econometrics, Elsevier, vol. 216(2), pages 450-493.
    25. Xanthi Pedeli & Anthony C. Davison & Konstantinos Fokianos, 2015. "Likelihood Estimation for the INAR( p ) Model by Saddlepoint Approximation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1229-1238, September.
    26. Cong Li & Dehui Wang & Fukang Zhu, 2019. "Detecting mean increases in zero truncated INAR(1) processes," International Journal of Production Research, Taylor & Francis Journals, vol. 57(17), pages 5589-5603, September.
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    Cited by:

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