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

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. (C) 2021 Elsevier B.V. All rights reserved.