Time Series Analysis
By Henrik Madsen, Boca Raton, Chapman & Hall/CRC, 2008, xv+380 pp., £39.99 or US$79.95 (hardback), ISBN 978-1420059670
Madsen's book is more than an introductory book of linear time series analysis. For example, the book's emphasis is on time domain methods, but the frequency domain approach is also given. In different chapters of the book, static systems, dynamic systems and time-varying systems are dealt with. In Chapter 3, static models are considered in the context of general linear models. Adaptive methods for estimation such as exponential smoothing, the Holt–Winter procedure and trend models are used. Dynamic systems can be deterministic or stochastic systems. Deter-ministic systems are studied through impulse response functions in Chapter 4. Chapter 5 considers stochastic processes. When using a rational transfer function such as the ARMA(p,q) and the ARIMA(p,d,q) process, Chapter 6 deals with identification, estimation and checking of these models. Chapter 7 gives the frequency domain approach. So-called transfer function models, in particular the Box–Jenkins transfer function model, are described in Chapter 8. Chapter 9 formulates the multivariate ARMA(p,q) process and state space models are explained in Chapter 10. Chapter 11 deals with recursive and adaptive methods for forecasting and control. Finally, the last chapter is devoted to problems inspired by real life and solutions to these problems can be found at www.imm.dtu.dk/~hm/time.series.analysis, where more additional exercises are also given.
The coverage of the book is broad and well synthesised. It follows classical material, but is clearly written and explained. Every chapter has additional exercises to promote better understanding by readers and solutions are also provided by the author. The book is well organised, and focused on overall results more than on details or proofs. However, and mainly in the first chapters, more numerical exercises are needed. I think that it is advisable to handle more simple illustrations to understand properly the book's contents. But above all, the weakness of the book is in the lack of software. There is neither mention nor comment or recommendation of using any statistical software. Nowadays, one cannot imagine conducting any statistical procedure without using specific software. I imagine that the author has intentionally left out such details, but I believe that using software deeply helps to overcome the intrinsic difficulty of explaining time series to beginners.
The reader needs some background in mathematical statistics and applied linear regression to make best use of the book, but it can be very useful for practitioners and students who are interested in this subject. The book is easy to read and provides essential material for understanding more complex dynamic systems. Summing up, it is a very interesting book and is highly recommended.