Bayesian Mixtures of Autoregressive Models

In this paper we propose a class of time-domain models for analyzing possibly nonstationary time series. This class of models is formed as a mixture of time series models, whose mixing weights are a function of time. We consider specifically mixtures of autoregressive models with a common but unknown lag. To make the methodology work we show that it is necessary to first partition the data into small non-overlapping segments, so that all observations within one segment are always allocated to the same component. The model parameters, including the number of mixture components, are then estimated via Markov chain Monte Carlo methods. The methodology is illustrated with simulated and real data. Supplemental materials are available online.