Bayesian time series and forecasting is a very broad field. This paper selectively notes some key models and ideas, leavened with extracts from a few time series analysis and forecasting examples. The latter parts of the paper link into and discuss a range of recent developments on specific modelling and applied topics in exciting and challenging areas of Bayesian time series analysis.

The author is grateful to Ioanna Manolopoulou and Emily Fox for comments on this chapter. This work was partly supported by grant DMS-1106516 from the U.S. National Science Foundation (NSF), and grants P50-GM081883 and RC1-AI086032 of the U.S National Institutes of Health. Any opinions, findings and conclusions or recommendations expressed in this work are those of the author and do not necessarily reflect the views of the NSF or the NIH.