Bayesian time-varying autoregressions: Theory, methods and applications

We review the class of time-varying autoregressive (TVAR) models and a range of related recent developments of Bayesian time series modelling. Beginning with TVAR models in a Bayesian dynamic linear modelling framework, we review aspects of latent structure analysis, including time-domain decomposition methods that provide inferences on the structure underlying non-stationary time series, and that are now central tools in the time series analyst's toolkit. Recent model extensions that deal with model order uncertainty, and are enabled using eÆcient Markov Chain Monte Carlo simulation methods, are discussed, as are novel approaches to sequential ltering and smoothing using particulate ltering methods. We emphasize the relevance of TVAR modelling in a range of applied contexts, including biomedical signal processing and communications, and highlight some of the central developments via examples arising in studies of multiple electroencephalographic (EEG) traces in neurophysiology. We conclude with comments about current research frontiers.