Bayesian analysis of multiple break-points threshold ARMA model with exogenous inputs

Abstract

In this paper, we introduce a Bayesian statistical inference approach for multiple break-points threshold autoregressive moving average model with exogenous inputs (MB-TARMAX) which change in state space and time domain. Based on the appropriate prior information of parameters, we give the full conditional posterior distribution of parameters including the thresholds and break-points. In order to obtain the estimates of parameters, we employ the Markov chain Monte Carlo (MCMC) method via Gibbs sampler with Metropolis-Hastings algorithm. Compared with Metropolis-Hastings algorithm, we apply Hamiltonian Monte Carlo algorithm to avoid the slow space exploration from simple random walk and improve the sampling efficiency. As applications, we demonstrate the effectiveness of our method from simulation experiments and a real example.

Keywords:

• Bayesian statistical inference
• MB-TARMAX model
• MCMC method
• Gibbs sampler
• Hamilton Monte Carlo algorithm
• Metropolis-Hastings algorithm

Acknowledgments

The authors thank the Editor and anonymous referees for carefully reading the manuscript and making helpful suggestions to improve its presentation.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11871377, 12071274).