Patterns hidden in a time series can reveal causal interactions, diagnose existing faults, and warn of impending failure. Discovering these patterns requires manipulating large amounts of data, which makes time series analysis one of the major applications of digital computers.

Early algorithms took one of two basic approaches. Time domain approaches, such as Box and Jenkins’s autocorrelation algorithms (1970), focus on relations within the data series under various time shifts. The Fourier transform allows the transformation of a time series to the frequency domain, which highlights the amplitude of the signal when filtered at various periodicities. This approach became computationally practical with the publication of the Cooley-Tukey algorithm for the fast Fourier transform, in 1965.

The frequency domain approach is widely used in many engineering applications, but recent advances in Bayesian inference have encouraged the development of new tools in the time domain. A time series can be viewed as a particularly simple form of a graphical probabilistic model in which each observation has a distribution conditioned on some subset of the preceding observations. Prado and West, while devoting one of their ten chapters to frequency domain analysis, concentrate on a range of advances in the time domain based on Bayesian methods. They cover not only conventional autoregression over stationary series, but also dynamic linear models, time-varying autoregressive models, mixture models and vector methods, and covariance models. They pay special attention to sequential Monte Carlo approaches to state-space modeling, including particle filtering and variations.

With the classroom in view, the authors present examples of each technique and provide a brief problem set for each chapter. The preface points to pages on each author’s Web site advertising datasets and software relevant to the book: Prado’s site (http://users.soe.ucsc.edu/~raquel/tsbook/) provides specific datasets discussed in the book, but no software; West’s (http://www.stat.duke.edu/~mw/tsbook/) offers a range of data and software, though not directly keyed to the book.

The book is written more as a summary reference than as an expository text, covering a wide range of techniques in a compact scope. The authors use certain sigla in a consistent manner throughout the book, but often define them only at the first reference; readers who want to dip into the discussion of a particular method without reading the earlier discussions would benefit from a central table of notation.

This volume will be valuable as an adjunct text in a graduate-level time series course and as a reference for anyone who works with temporal data.