Bayesian estimation and model selection of a multivariate smooth transition autoregressive model

The multivariate smooth transition autoregressive model with order k (M‐STAR)(k) is a nonlinear multivariate time series model able to capture regime changes in the conditional mean. The main aim of this paper is to develop a Bayesian estimation scheme for the M‐STAR(k) model that includes the coefficient parameter matrix, transition function parameters, covariance parameter matrix, and the model order k as parameters to estimate. To achieve this aim, the joint posterior distribution of the parameters for the M‐STAR(k) model is derived. The conditional posterior distributions are then shown, followed by the design of a posterior simulator using a combination of Markov chain Monte Carlo (MCMC) algorithms that includes the Metropolis‐Hastings, Gibbs sampler, and reversible jump MCMC algorithms. Following this, extensive simulation studies, as well as case studies, are detailed at the end.