Nonlinear Time Series Analysis

Book Description

Deterministic chaos provides a novel framework for the analysis of irregular time series. Traditionally, nonperiodic signals are modeled by linear stochastic processes. But even very simple chaotic dynamical systems can exhibit strongly irregular time evolution without random inputs. Chaos theory offers completely new concepts and algorithms for time series analysis which can lead to a thorough understanding of the signal. The book introduces a broad choice of such concepts and methods, including phase space embeddings, nonlinear prediction and noise reduction, Lyapunov exponents, dimensions and entropies, as well as statistical tests for nonlinearity. Related topics like chaos control, wavelet analysis and pattern dynamics are also discussed. Applications range from high quality, strictly deterministic laboratory data to short, noisy sequences which typically occur in medicine, biology, geophysics or the social sciences. All material is discussed and illustrated using real experimental data.

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The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

Customer Reviews:

Good for both beginners and advanced practitioners.......2003-10-22

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.

Excellent for practitioners.......2001-02-23

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...

Book Description

Recently, a great deal of progress has been made in the modeling and understanding of processes with nonlinear dynamics, even when only time series data are available. Modern reconstruction theory deals with creating nonlinear dynamical models from data and is at the heart of this improved understanding. Most of the work has been done by dynamicists, but for the subject to reach maturity, statisticians and signal processing engineers need to provide input both to the theory and to the practice. The book brings together different approaches to nonlinear time series analysis in order to begin a synthesis that will lead to better theory and practice in all the related areas. This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.

Nonlinear Time Series Analysis: Methods and Applications (Nonlinear Time Series and Chaos)

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Passion
Extremely disappointing.
Dramatic, chaotic and yet analytic.

Nonlinear Time Series Analysis: Methods and Applications (Nonlinear Time Series and Chaos)
Cees Diks
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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Customer Reviews:

Passion.......2001-03-02

Of course there are many books dealing with the relationship between non-linear time series and chaos. It resembles the situation where one has to choose among two women that you both love, but after spending a weekend without passion with one of them, you know where to go for. After reading the book by Diks, and comparing it to related work, I can only come to the conclusion that it stands out. The book is clear, well written, and obviously relevant to theorists working in such divergent fields as statistics, finance, and physics. To each professor supervising a Ph.D. student I would therefore like to say: put it on the required reading list and if necessary use to force to make them on the subjects discussed by Diks.

Extremely disappointing........2001-02-26

This is not my first book about nonlinear time series and chaos theory and really i'm just wondering how it get published. I'm trying to find something positive to say but i cannot. I cannot recall what i did learn from it: just one thing, testing for reversibility. Ok, that's rather short for a book, a paper would have been sufficient, and less costly. I've just wasted my money on this. In addition, i'm not the kind of reviewer who is used to give 1 star to a good book, it has to be very bad to get that.

Rather go to Kantz or Abarbanel for useful books on nonlinear time series analysis...

Dramatic, chaotic and yet analytic........2000-05-04

Seldomly I have read a book on this subject which was so clear and well written. Diks turns out to be a captivating writer, who does not scare away from truth, equations, or Greek letters. I'm waiting for part 2, to see how the story ends.

Nonlinear Time Series: Nonparametric and Parametric Methods (Springer Series in Statistics)

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Well used already!

Nonlinear Time Series: Nonparametric and Parametric Methods (Springer Series in Statistics)
Jianqing Fan , and Qiwei Yao
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 0387261427

Book Description

This book presents the contemporary statistical methods and theory of nonlinear time series analysis. The principal focus is on nonparametric and semiparametric techniques developed in the last decade. It covers the techniques for modelling in state-space, in frequency-domain as well as in time-domain. To reflect the integration of parametric and nonparametric methods in analyzing time series data, the book also presents an up-to-date exposure of some parametric nonlinear models, including ARCH/GARCH models and threshold models. A compact view on linear ARMA models is also provided. Data arising in real applications are used throughout to show how nonparametric approaches may help to reveal local structure in high-dimensional data. Important technical tools are also introduced. The book will be useful for graduate students, application-oriented time series analysts, and new and experienced researchers. It will have the value both within the statistical community and across a broad spectrum of other fields such as econometrics, empirical finance, population biology and ecology. The prerequisites are basic courses in probability and statistics. Jianqing Fan, coauthor of the highly regarded book Local Polynomial Modeling, is Professor of Statistics at the University of North Carolina at Chapel Hill and the Chinese University of Hong Kong. His published work on nonparametric modeling, nonlinear time series, financial econometrics, analysis of longitudinal data, model selection, wavelets and other aspects of methodological and theoretical statistics has been recognized with the Presidents' Award from the Committee of Presidents of Statistical Societies, the Hettleman Prize for Artistic and Scholarly Achievement from the University of North Carolina, and by his election as a fellow of the American Statistical Association and the Institute of Mathematical Statistics. Qiwei Yao is Professor of Statistics at the London School of Economics and Political Science. He is an elected member of the International Statistical Institute, and has served on the editorial boards for the Journal of the Royal Statistical Society (Series B) and the Australian and New Zealand Journal of Statistics.

Customer Reviews:

Well used already!.......2006-08-31

This is an excellent monograph. The authors have provided an up-to-date analysis of parametric and nonparametric methods with a comprehensive bibliography. The book is very readible. The authors combine elements of descriptive overview, nontrivial examples and theorems / proofs.

Nonlinear Time Series: Semiparametric and Nonparametric Methods (Monographs on Statistics and Applied Probability)

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Nonlinear Time Series: Semiparametric and Nonparametric Methods (Monographs on Statistics and Applied Probability)
Jiti Gao
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 1584886137

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Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Answering the call for an up-to-date overview of the latest developments in the field, Nonlinear Time Series: Semiparametric and Nonparametric Methods focuses on various semiparametric methods in model estimation, specification testing, and selection of time series data. After a brief introduction, the book examines semiparametric estimation and specification methods and then applies these approaches to a class of nonlinear continuous-time models with real-world data. It also assesses some newly proposed semiparametric estimation procedures for time series data with long-range dependence. Even though the book only deals with climatological and financial data, the estimation and specifications methods discussed can be applied to models with real-world data in many disciplines. This resource covers key methods in time series analysis and provides the necessary theoretical details. The latest applied finance and financial econometrics results and applications presented in the book enable researchers and graduate students to keep abreast of developments in the field.

Nonlinear Modelling of High Frequency Financial Time Series (Financial Economics and Quantitative Analysis Series)

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Nonlinear Modelling of High Frequency Financial Time Series (Financial Economics and Quantitative Analysis Series)

Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471974641

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Nonlinear Modelling of High Frequency Financial Time Series Edited by Christian Dunis and Bin Zhou In the competitive and risky environment of today's financial markets, daily prices and models based upon low frequency price series data do not provide the level of accuracy required by traders and a growing number of risk managers. To improve results, more and more researchers and practitioners are turning to high frequency data. Nonlinear Modelling of High Frequency Financial Time Series presents the latest developments and views of leading international researchers and market practitioners, in modelling high frequency data in finance. Combining both nonlinear modelling and intraday data for financial markets, the editors provide a fascinating foray into this extremely popular discipline. This book evolves around four major themes. The first introductory section focuses on high frequency financial data. The second part examines the exact nature of the time series considered: several linearity tests are presented and applied and their modelling implications assessed. The third and fourth parts are dedicated to modelling and forecasting these financial time series.

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Nonlinear Time Series
Jianqing Fan , and Qiwei Yao
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387951709

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Transformations Through Space and Time: An Analysis of Nonlinear Structures, Bifurcation Points and Autoregressive Dependencies (Nato Science Series D:)

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Transformations Through Space and Time: An Analysis of Nonlinear Structures, Bifurcation Points and Autoregressive Dependencies (Nato Science Series D:)

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 9024733626

Time-Domain Computer Analysis of Nonlinear Hybrid Systems

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Time-Domain Computer Analysis of Nonlinear Hybrid Systems
Wenquan Sui
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0849313961

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The analysis of nonlinear hybrid electromagnetic systems poses significant challenges that essentially demand reliable numerical methods. In recent years, research has shown that finite-difference time-domain (FDTD) cosimulation techniques hold great potential for future designs and analyses of electrical systems. Time-Domain Computer Analysis of Nonlinear Hybrid Systems summarizes and reviews more than 10 years of research in FDTD cosimulation. It first provides a basic overview of the electromagnetic theory, the link between field theory and circuit theory, transmission line theory, finite-difference approximation, and analog circuit simulation. The author then extends the basic theory of FDTD cosimulation to focus on techniques for time-domain field solving, analog circuit analysis, and integration of other lumped systems, such as n-port nonlinear circuits, into the field-solving scheme. The numerical cosimulation methods described in this book and proven in various applications can effectively simulate hybrid circuits that other techniques cannot. By incorporating recent, new, and previously unpublished results, this book effectively represents the state of the art in FDTD techniques. More detailed studies are needed before the methods described are fully developed, but the discussions in this book build a good foundation for their future perfection.

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