Nonlinear Time Series Analysis [Paperback]

This book provides an excellent overview of chaos theory concepts applied to time series analysis. First part constitutes a good tutorial on chaos theory and its implications on time series analysis while the second part discusses in detail aspects of time-series related chaos theory concepts (with an historical perspective of the related research). Time series analysts will certainly benefit from it thanks to its balanced exposition of issues of chaos theory concepts for non-infinite data sets...

However, the only drawback is that it essentially deals with deterministic systems, not stochastic ones. But if you gathered your data on a physical system, it's OK.

In my search for good material on time series analysis, I have come across many books packed with information, yet so dry as to make them unreadable (readers of Hamilton's "Time Series Analysis" will know what I mean - Amazing book, but unreadably boring).

Kantz and Schreiber do not suffer from that all too common problem. They write clearly and in a very readable style. Their use of real-world datasets and numerous (though not overwhelming) charts makes their work quickly accessible even to beginniners in the field. They provide enough mathematical formalisms to make use of what they present, but not so many as to require a PhD in math to follow the flow of the text. For more advanced readers, they cover a wide range of topics useful both for analysis and for forecasting. Chapter 12, in particular, opened me to a whole world of new techniques.

As my one negative comment on this book, I would have liked that same chapter 12 fleshed out more, to the point that I would buy a follow-up book covering nothing but an elaboration on that single chapter.

If you have an interest in time series analysis and forecasting, and have grown tired of dry material that provides nothing more than yet another extension to ARIMA or Kalman filtering, you will love this book.

I only write this review to repudiate a previous reviewer's comment that this is a good book on "chaos". No, it is not. There is no detailed 'first-principles' description of ANYTHING that forms the theoretical basis of deterministic dynamical systems. So, don't buy this book for a first-glance at analysis of dynamics in chaotic systems! (Typically, I assume, one needs to understand the theory before attempting to decipher experiments. Try the books by Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in nonlinearity) Strogatz or Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists Thompson-Stewart or Chaos Tsonis, for a structured forage into theoretical chaos)

What this book is, is a review/collection of revised manuscripts of some fine articles published by the authors and others who were looking to quantify the experimentally-observed dynamics of chaotic systems. The first edition (1999) of this book is more of a collection of notes, but the second edition is far more comprehensive and well-structured.

The target audience for this book are advanced graduate students who are acquainted with the theory governing nonlinear dynamical systems, undergrad-level stats and advanced linear algebra (topics in topology?). (This 'target audience' description is not didactic as I myself did (do) not know much about either topology or stats before working with this book.)

As the analysis of any experiment is truly just an exercise in statistics, this book expects a broad familiarity with statistical methods. This book is not a general collection of tools that can be applied to every signal out there. So it is expected that the reader already possesses a highly nonlinear/weakly stationary signal that they are interested in deciphering. The authors also provide an online repository of some data sets and routines used as examples in the book (TISEAN package?).

This book steps the reader through specific flavors of embedding, false neighbors counting, linear and nonlinear forecasting techniques through the chapters. In spite of that, most chapters can be used as stand-alone monographs with few continuity issues.

I find the references at the end of each chapter to be sufficient.

Over all, I find this book extremely useful and I have both the two editions in my library. Like most books however a negative feature of this book is that it takes its time in getting to the point (which sometimes gets spread between chapters). I found reading the original articles, cited in a section, before reading that section in the book itself to be particularly helpful.

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