A range of developments in Bayesian time series modelling in recent years has focussed on issues of identifying latent structure in time series. This has led to new uses and interpretations of existing theory for latent process decompositions of dynamic models, and to new models for univariate and multivariate time series. This article draws together concepts and modelling approaches that are central to applications of time series decomposition methods, and reviews recent modelling and applied developments. Several applications in time series analyses in geology, climatology, psychiatry and finance are discussed, as are related modelling directions and current research frontiers.

The research reported here was partially supported by NSF grants DMS-9704432 and DMS-9707914.

Invited paper for the Sixth Valencia International Meeting on Bayesian Statistics (May 30-June 4 1998, Las Fuentes, Spain)

The manuscript is available in either postscript or pdf

The reply to discussants is also available in either postscript or pdf