On MCMC sampling in random coefficients self-exciting integer-valued threshold autoregressive processes

Abstract

In this study, Bayesian estimation is performed for a class of random coefficient self-exciting integer-valued threshold autoregressive processes with explanatory variables. A new model with a linear structure is obtained through model reconstruction, which makes Markov Chain Monte Carlo method easy to perform. By introducing the latent variables series, a complete data likelihood is obtained. Based on this likelihood, the full conditional distributions are easily obtained for all the parameters and latent variables. By maximizing the posterior probability function, the threshold parameter is accurately estimated. Finally, some numerical results of the estimates and a real data example of crime counts in Ballina, New South Wales, Australia are presented.

Keywords:

• Integer-valued threshold autoregressive models
• random coefficients process
• Bayesian inference
• MCMC sampling
• latent variable

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11901053], Natural Science Foundation of Jilin Province [grant numbers 20220101038JC, 20230201078GX, YDZJ202301ZYTS393, 20210101149JC], Postdoctoral Foundation of Jilin Province [grant number 2023337], Scientific Research Project of Jilin Provincial Department of Education [grant numbers JJKH20220671KJ, JJKH20230665KJ].