We present classes of Bayesian mixture models for non-linear auto-regressive times series, based on developments in semi-parametric Bayesian density estimation in recent years. The development involves formal classes of multivariate discrete mixture distributions, providing flexibility in modelling arbitrary non-linearities in time series structure and a formal inferential framework within which to address the problems of inference and prediction. The models relate naturally to existing kernel and related methods, threshold models and others, though offer major advances in terms of parameter estimation and predictive calculations. Theoretical and computational aspects are developed here, the latter involving efficient simulation of posterior and predictive distributions. Various examples illustrate our perspectives on identification and inference using this mixture approach.

The manuscript is available in pdf format. This paper appeared in the Journal of Time Series Analysis, 18 (1997): 593-614.