Abstract
We examine a trivariate time series model that is subject to a regime switch, where the shifts are governed by an unobserved, two-state variable that follows a Markov process. The analysis is performed in a Bayesian framework developed by Albert and Chib (1993), where the unobserved states are treated as missing data and then analyzed via Gibbs sampling.
This approach generates the posterior conditional distribution of all the parameters given the hidden states, and the posterior conditional distribution of the states given the parameters. This allows us to obtain the estimated values of all the parameters of interest.