Nonlinear Time Series Analysis

Author: Holger Kantz
Publisher: Cambridge University Press
ISBN: 0521529026
Release Date: 2004
Genre: Mathematics

New edition of a successful advanced text on nonlinear time series analysis.

Nonlinear Time Series Analysis

Author: Holger Kantz
Publisher: Cambridge University Press
ISBN: 9781139440431
Release Date: 2003-11-27
Genre: Science

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.

Nonlinear Time Series Analysis

Author: Holger Kantz
Publisher:
ISBN: 0521821509
Release Date: 2004
Genre: Science

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.

Nonlinear Time Series Analysis with R

Author: Ray Huffaker
Publisher: Oxford University Press
ISBN: 9780191085796
Release Date: 2017-09-28
Genre: Mathematics

Nonlinear Time Series Analysis with R provides a practical guide to emerging empirical techniques allowing practitioners to diagnose whether highly fluctuating and random appearing data are most likely driven by random or deterministic dynamic forces. It joins the chorus of voices recommending 'getting to know your data' as an essential preliminary evidentiary step in modelling. Time series are often highly fluctuating with a random appearance. Observed volatility is commonly attributed to exogenous random shocks to stable real-world systems. However, breakthroughs in nonlinear dynamics raise another possibility: highly complex dynamics can emerge endogenously from astoundingly parsimonious deterministic nonlinear models. Nonlinear Time Series Analysis (NLTS) is a collection of empirical tools designed to aid practitioners detect whether stochastic or deterministic dynamics most likely drive observed complexity. Practitioners become 'data detectives' accumulating hard empirical evidence supporting their modelling approach. This book is targeted to professionals and graduate students in engineering and the biophysical and social sciences. Its major objectives are to help non-mathematicians—with limited knowledge of nonlinear dynamics—to become operational in NLTS; and in this way to pave the way for NLTS to be adopted in the conventional empirical toolbox and core coursework of the targeted disciplines. Consistent with modern trends in university instruction, the book makes readers active learners with hands-on computer experiments in R code directing them through NLTS methods and helping them understand the underlying logic. The computer code is explained in detail so that readers can adjust it for use in their own work. The book also provides readers with an explicit framework—condensed from sound empirical practices recommended in the literature—that details a step-by-step procedure for applying NLTS in real-world data diagnostics.

Applied Nonlinear Time Series Analysis

Author: Michael Small
Publisher: World Scientific
ISBN: 9812567771
Release Date: 2005
Genre: Science

Nonlinear time series methods have developed rapidly over a quarter of a century and have reached an advanced state of maturity during the last decade. Implementations of these methods for experimental data are now widely accepted and fairly routine; however, genuinely useful applications remain rare. This book focuses on the practice of applying these methods to solve real problems. To illustrate the usefulness of these methods, a wide variety of physical and physiological systems are considered. The technical tools utilized in this book fall into three distinct, but interconnected areas: quantitative measures of nonlinear dynamics, MonteOCoCarlo statistical hypothesis testing, and nonlinear modeling. Ten highly detailed applications serve as case studies of fruitful applications and illustrate the mathematical techniques described in the text."

Elements of Nonlinear Time Series Analysis and Forecasting

Author: Jan G. De Gooijer
Publisher: Springer
ISBN: 9783319432526
Release Date: 2017-04-24
Genre: Mathematics

This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a “theorem-proof” format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time series and at the same time also includes interesting material for more advanced readers. Though it is largely self-contained, readers require an understanding of basic linear time series concepts, Markov chains and Monte Carlo simulation methods. The book covers time-domain and frequency-domain methods for the analysis of both univariate and multivariate (vector) time series. It makes a clear distinction between parametric models on the one hand, and semi- and nonparametric models/methods on the other. This offers the reader the option of concentrating exclusively on one of these nonlinear time series analysis methods. To make the book as user friendly as possible, major supporting concepts and specialized tables are appended at the end of every chapter. In addition, each chapter concludes with a set of key terms and concepts, as well as a summary of the main findings. Lastly, the book offers numerous theoretical and empirical exercises, with answers provided by the author in an extensive solutions manual.

Nonlinear Time Series Analysis of Business Cycles

Author: Costas Milas
Publisher: Emerald Group Publishing
ISBN: 9780444518385
Release Date: 2006
Genre: Business & Economics

The business cycle has long been the focus of empirical economic research. Until recently statistical analysis of macroeconomic fluctuations was dominated by linear time series methods. Over the past 15 years, however, economists have increasingly applied tractable parametric nonlinear time series models to business cycle data; most prominent in this set of models are the classes of Threshold AutoRegressive (TAR) models, Markov-Switching AutoRegressive (MSAR) models, and Smooth Transition AutoRegressive (STAR) models. In doing so, several important questions have been addressed in the literature, including: 1. Do out-of-sample (point, interval, density, and turning point) forecasts obtained with nonlinear time series models dominate those generated with linear models? 2. How should business cycles be dated and measured? 3. What is the response of output and employment to oil-price and monetary shocks? 4. How does monetary policy respond to asymmetries over the business cycle? 5. Are business cycles due more to permanent or to transitory negative shocks? 6. Is the business cycle asymmetric, and does it matter? Accordingly, we have compiled and edited a book for the Elsevier economics program comprising 15 original papers on these and related themes. *Contributions to Economic Analysis was established in 1952 *The series purpose is to stimulate the international exchange of scientific information *The series includes books from all areas of macroeconomics and microeconomics

Nonlinear Time Series Analysis in the Geosciences

Author: Reik V. Donner
Publisher: Springer Science & Business Media
ISBN: 9783540789376
Release Date: 2008-08-18
Genre: Science

The understanding of dynamical processes in the complex system “Earth” requires the appropriate analysis of a large amount of data from observations and/or model simulations. In this volume, modern nonlinear approaches are introduced and used to study specifiic questions relevant to present-day geoscience. The approaches include spatio-temporal methods, time-frequency analysis, dimension analysis (in particular, for multivariate data), nonlinear statistical decomposition, methods designed for treating data with uneven sampling or missing values, nonlinear correlation and synchronization analysis, surrogate data techniques, network approaches, and nonlinear methods of noise reduction. This book aims to present a collection of state-of-the-art scientific contributions used in current studies by some of the world's leading scientists in this field.

Nonlinear Time Series

Author: Jianqing Fan
Publisher: Springer Science & Business Media
ISBN: 0387693955
Release Date: 2008-09-11
Genre: Mathematics

This is the first book that integrates useful parametric and nonparametric techniques with time series modeling and prediction, the two important goals of time series analysis. Such a book will benefit researchers and practitioners in various fields such as econometricians, meteorologists, biologists, among others who wish to learn useful time series methods within a short period of time. The book also intends to serve as a reference or text book for graduate students in statistics and econometrics.

Nonlinear Time Series Analysis

Author: Ruey S. Tsay
Publisher: Wiley
ISBN: 9781119264057
Release Date: 2018-10-09
Genre: Mathematics

A comprehensive resource that draws a balance between theory and applications of nonlinear time series analysis Nonlinear Time Series Analysis offers an important guide to both parametric and nonparametric methods, nonlinear state-space models, and Bayesian as well as classical approaches to nonlinear time series analysis. The authors—noted experts in the field—explore the advantages and limitations of the nonlinear models and methods and review the improvements upon linear time series models. The need for this book is based on the recent developments in nonlinear time series analysis, statistical learning, dynamic systems and advanced computational methods. Parametric and nonparametric methods and nonlinear and non-Gaussian state space models provide a much wider range of tools for time series analysis. In addition, advances in computing and data collection have made available large data sets and high-frequency data. These new data make it not only feasible, but also necessary to take into consideration the nonlinearity embedded in most real-world time series. This vital guide: • Offers research developed by leading scholars of time series analysis • Presents R commands making it possible to reproduce all the analyses included in the text • Contains real-world examples throughout the book • Recommends exercises to test understanding of material presented • Includes an instructor solutions manual and companion website Written for students, researchers, and practitioners who are interested in exploring nonlinearity in time series, Nonlinear Time Series Analysis offers a comprehensive text that explores the advantages and limitations of the nonlinear models and methods and demonstrates the improvements upon linear time series models.

Nonlinear Time Series Analysis of Economic and Financial Data

Author: Philip Rothman
Publisher: Springer Science & Business Media
ISBN: 9781461551294
Release Date: 2012-12-06
Genre: Business & Economics

Nonlinear Time Series Analysis of Economic and Financial Data provides an examination of the flourishing interest that has developed in this area over the past decade. The constant theme throughout this work is that standard linear time series tools leave unexamined and unexploited economically significant features in frequently used data sets. The book comprises original contributions written by specialists in the field, and offers a combination of both applied and methodological papers. It will be useful to both seasoned veterans of nonlinear time series analysis and those searching for an informative panoramic look at front-line developments in the area.

Nonlinear Time Series

Author: Randal Douc
Publisher: CRC Press
ISBN: 9781466502345
Release Date: 2014-01-06
Genre: Mathematics

Designed for researchers and students, Nonlinear Times Series: Theory, Methods and Applications with R Examples familiarizes readers with the principles behind nonlinear time series models—without overwhelming them with difficult mathematical developments. By focusing on basic principles and theory, the authors give readers the background required to craft their own stochastic models, numerical methods, and software. They will also be able to assess the advantages and disadvantages of different approaches, and thus be able to choose the right methods for their purposes. The first part can be seen as a crash course on "classical" time series, with a special emphasis on linear state space models and detailed coverage of random coefficient autoregressions, both ARCH and GARCH models. The second part introduces Markov chains, discussing stability, the existence of a stationary distribution, ergodicity, limit theorems, and statistical inference. The book concludes with a self-contained account on nonlinear state space and sequential Monte Carlo methods. An elementary introduction to nonlinear state space modeling and sequential Monte Carlo, this section touches on current topics, from the theory of statistical inference to advanced computational methods. The book can be used as a support to an advanced course on these methods, or an introduction to this field before studying more specialized texts. Several chapters highlight recent developments such as explicit rate of convergence of Markov chains and sequential Monte Carlo techniques. And while the chapters are organized in a logical progression, the three parts can be studied independently. Statistics is not a spectator sport, so the book contains more than 200 exercises to challenge readers. These problems strengthen intellectual muscles strained by the introduction of new theory and go on to extend the theory in significant ways. The book helps readers hone their skills in nonlinear time series analysis and their applications.

Topics in Nonlinear Time Series Analysis

Author: Andreas Galka
Publisher: World Scientific
ISBN: 9789814493925
Release Date: 2000-02-18
Genre: Science

This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of the underlying dynamics, as introduced by nonlinear dynamics. In particular, current algorithms for state space reconstruction, correlation dimension estimation, testing for determinism and surrogate data testing are presented — algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980. Special emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram. Contents:Dynamical Systems, Time Series and AttractorsLinear MethodsState Space Reconstruction: Theoretical FoundationsState Space Reconstruction: Practical ApplicationDimensions: Basic DefinitionsLyapunov Exponents and EntropiesNumerical Estimation of the Correlation DimensionSources of Error and Data Set Size RequirementsMonte Carlo Analysis of Dimension EstimationSurrogate Data TestsDimension Analysis of the Human EEGTesting for Determinism in Time Series Readership: Graduates and scientists in physics, applied mathematics, neurology, theoretical biology, economics, meteorology and neuroinformatics. Keywords:Time Series Analysis;Nonlinear Dynamics;Fractal Dimension;Correlation Dimension;Chaos;Electroencephalogram;EEG;Determinism;Strange Attractor;Embedding;Attractor Reconstruction;Surrogate DataReviews: “The book is pleasantly written and makes for easy reading. It is informative for anyone with a sufficiently deep knowledge of nonlinear dynamics.” Mathematical Reviews

Nonlinear Time Series

Author: Jiti Gao
Publisher: CRC Press
ISBN: 1420011219
Release Date: 2007-03-22
Genre: Mathematics

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.