Applied time series analysis

Applied time series analysis, by Wayne A. Woodward, Henry L. Gray and Alan C. Elliott, Boca Raton, FL, CRC Press, 2011, xxiii+ 540 pp., £60.99 or US$99.95 (hardback), ISBN 978-1-4398-1837-4

This book, with its 13 chapters, discusses many older and more recent time series models in both the time and frequency domains and includes theory, methods and real-life applications. It discusses all stages of the analysis of such data, which are model identification, estimation, building and forecasting.

The book is organised as follows. Chapters 1–4 discuss stationary time series models, such as ARMA, ARCH and GARCH models of various orders, and some characteristics of these models including their autocorrelation, spectral density and spectrum with their properties and estimators. Chapter 5 investigates non-stationary time series models including ARIMA, ARUMA, and multiplicative seasonal models and random walks. Chapters 6–9 discuss aspects of analysing all the models above: identification of the model order, estimation of the model parameters, and model checking and forecasting. Multivariate versions of most of the univariate time series models above are described in Chapter 10, involving state-space models. Chapter 11 looks at long-memory processes that have long-range-dependent time series data, including FARMA and GARMA models with their autocorrelations and spectral densities. The last two chapters discuss techniques for analysing non-stationary time series models with time-varying frequencies. The two techniques discussed are using wavelets and converting such models to generalised-stationary processes that contain the multiplicative-stationary processes.

The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book's material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis. A simple criticism of the book is that it does not mention non-Gaussian time series 1, particularly integer-valued time series.

http://dx.doi.org/10.1080/02664763.2012.682445