Mixture models in time series

This chapter concerns mixture models in time series analysis. Examples include Markov switching models, mixtures of dynamic linear models (DLMs) also known as multi-process models, and examples of nonlinear and/or non-Gaussian models that can be approximated with normal mixtures of some form. Bayesian analysis using such models can employ computational strategies that exploit the conditionally normal, linear model structures implied by expansion of the parameter space to include the inherent latent “mixing” variables. These models and inference methods are developed and exemplified. Two detailed illustrations involve an analysis of electroencephalogram signals via mixtures of autoregressive processes, and an analysis of daily returns on exchange rates via stochastic volatility models.