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

On MCMC sampling in self-exciting integer-valued threshold time series models. (English) Zbl 07476343

Comput. Stat. Data Anal. 169, Article ID 107410, 13 p. (2022).
Summary: 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.

Cited in 11 Documents

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F15 Bayesian inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
62-08 Computational methods for problems pertaining to statistics

Keywords:

integer-valued time series; threshold autoregressive model; Bayesian inference; MCMC sampling; latent variables

Software:

Bolstad
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Full Text: DOI

References:

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