Markov-switching quantile autoregression: a Gibbs sampling approach

We extend the class of linear quantile autoregression models by allowing for the possibility of Markov-switching regimes in the conditional distribution of the response variable. We also develop a Gibbs sampling approach for posterior inference by using data augmentation and a location-scale mixture representation of the asymmetric Laplace distribution. Bayesian calculations are easily implemented, because all complete conditional densities used in the Gibbs sampler have closed-form expressions. The proposed Gibbs sampler provides the basis for a stepwise re-estimation procedure that ensures non-crossing quantiles. Monte Carlo experiments and an empirical application to the U.S. real interest rate show that both inference and forecasting are improved when the quantile monotonicity restriction is taken into account.