Mixture autoregressive (MAR) models provide a flexible way to model time\nseries with predictive distributions which depend on the recent history of the\nprocess and are able to accommodate asymmetry and multimodality. Bayesian\ninference for such models offers the additional advantage of incorporating the\nuncertainty in the estimated models into the predictions. We introduce a new\nway of sampling from the posterior distribution of the parameters of MAR models\nwhich allows for covering the complete parameter space of the models, unlike\nprevious approaches. We also propose a relabelling algorithm to deal a\nposteriori with label switching. We apply our new method to simulated and real\ndatasets, discuss the accuracy and performance of our new method, as well as\nits advantages over previous studies. The idea of density forecasting using\nMCMC output is also introduced.\n