This is the second edition of a popular graduate level textbook on time series modeling, computation and inference. The book is essentially unique in its approach, with a focus on Bayesian methods, although classical methods are also covered. The second edition has been updated with an additional author, new references throughout, and new material on multivariate time series. There are also lots of new examples and exercises, and the computing has been greatly enhanced. Code, data, and other material are now made available on a supplementary website.