BAYESIAN TIME-VARYING AUTOREGRESSIONS: THEORY, METHODS
AND APPLICATIONS
Raquel Prado, Gabriel Huerta and Mike West
August 2000
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 efficient Markov Chain Monte Carlo simulation
methods, are discussed, as are novel approaches to sequential
filtering and smoothing using particulate filtering 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.
Keywords:
Bayesian analysis; Dynamic linear models;
Model uncertainty; MCMC simulation; Time series decompositions; TVAR models
The manuscript is available in postscript and
pdf formats