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Nonlinear Time Series

Nonparametric and Parametric Methods

Author: Jianqing Fan,Qiwei Yao

Publisher: Springer Science & Business Media

ISBN: 9780387693958

Category: Mathematics

Page: 552

View: 1815

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.
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Nonlinear Time Series Analysis in the Geosciences

Applications in Climatology, Geodynamics and Solar-Terrestrial Physics

Author: Reik V. Donner,Susana M. Barbosa

Publisher: Springer Science & Business Media

ISBN: 3540789375

Category: Science

Page: 390

View: 6482

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.
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Nonlinear Time Series Analysis

Author: Ruey S. Tsay,Rong Chen

Publisher: Wiley

ISBN: 1119264057

Category: Mathematics

Page: 512

View: 7724

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.
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Nonlinear Time Series

Theory, Methods and Applications with R Examples

Author: Randal Douc,Eric Moulines,David Stoffer

Publisher: CRC Press

ISBN: 1466502258

Category: Mathematics

Page: 551

View: 4454

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.
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Nonlinear Time Series Analysis of Business Cycles

Author: Costas Milas,Philip Rothman,Dick van Dijk

Publisher: Emerald Group Publishing

ISBN: 044451838X

Category: Business & Economics

Page: 435

View: 2298

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
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Elements of Nonlinear Time Series Analysis and Forecasting

Author: Jan G. De Gooijer

Publisher: Springer

ISBN: 3319432524

Category: Mathematics

Page: 618

View: 3750

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.
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Applied Nonlinear Time Series Analysis

Applications in Physics, Physiology and Finance

Author: Michael Small

Publisher: World Scientific

ISBN: 9789812567772

Category: Science

Page: 245

View: 3442

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."
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Nonlinear Time Series

Semiparametric and Nonparametric Methods

Author: Jiti Gao

Publisher: CRC Press

ISBN: 9781420011210

Category: Mathematics

Page: 237

View: 7968

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.
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Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis

A Frequency Domain Approach

Author: György Terdik

Publisher: Springer Science & Business Media

ISBN: 9780387988726

Category: Mathematics

Page: 260

View: 9353

"The book should prove valuable to students interested in nonlinear time series analysis and applications, to research workers is nonlinear stochastic analysis, and to people interested in practical data analysis."--BOOK JACKET.
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Topics in Nonlinear Time Series Analysis

With Implications for EEG Analysis

Author: Andreas Galka

Publisher: World Scientific

ISBN: 9789810241483

Category: Mathematics

Page: 342

View: 5346

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.
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Nonlinear Time Series Analysis with Applications to Foreign Exchange Rate Volatility

Author: Christian Hafner

Publisher: Springer Science & Business Media

ISBN: 3662126052

Category: Business & Economics

Page: 222

View: 1919

The book deals with the econometric analysis of high frequency financial time series. It emphasizes a new nonparametric approach to volatility models and provides theoretical and empirical comparisons with conventional ARCH models, applied to foreign exchange rates. Nonparametric models are discussed that cope with asymmetry and long memory of volatility as well as heterogeneity of higher conditional moments.
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A Nonlinear Time Series Workshop

A Toolkit for Detecting and Identifying Nonlinear Serial Dependence

Author: Douglas M. Patterson,Richard A. Ashley

Publisher: Springer Science & Business Media

ISBN: 144198688X

Category: Business & Economics

Page: 201

View: 7595

The complex dynamic behavior exhibited by many nonlinear systems - chaos, episodic volatility bursts, stochastic regimes switching - has attracted a good deal of attention in recent years. A Nonlinear Time Series Workshop provides the reader with both the statistical background and the software tools necessary for detecting nonlinear behavior in time series data. The most useful existing detection techniques are described, including Engle's LaGrange Multiplier test for conditional hetero-skedasticity and tests based on the correlation dimension and on the estimated bispectrum. These techniques are illustrated using actual data from fields such as economics, finance, engineering, and geophysics.
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Robust and Nonlinear Time Series Analysis

Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 “Stochastische Mathematische Modelle”, Heidelberg 1983

Author: J. Franke,W. Härdle,D. Martin

Publisher: Springer Science & Business Media

ISBN: 1461578213

Category: Mathematics

Page: 286

View: 6459

Classical time series methods are based on the assumption that a particular stochastic process model generates the observed data. The, most commonly used assumption is that the data is a realization of a stationary Gaussian process. However, since the Gaussian assumption is a fairly stringent one, this assumption is frequently replaced by the weaker assumption that the process is wide~sense stationary and that only the mean and covariance sequence is specified. This approach of specifying the probabilistic behavior only up to "second order" has of course been extremely popular from a theoretical point of view be cause it has allowed one to treat a large variety of problems, such as prediction, filtering and smoothing, using the geometry of Hilbert spaces. While the literature abounds with a variety of optimal estimation results based on either the Gaussian assumption or the specification of second-order properties, time series workers have not always believed in the literal truth of either the Gaussian or second-order specifica tion. They have none-the-less stressed the importance of such optimali ty results, probably for two main reasons: First, the results come from a rich and very workable theory. Second, the researchers often relied on a vague belief in a kind of continuity principle according to which the results of time series inference would change only a small amount if the actual model deviated only a small amount from the assum ed model.
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Nonlinear Time Series Analysis of Economic and Financial Data

Author: Philip Rothman

Publisher: Springer Science & Business Media

ISBN: 1461551293

Category: Business & Economics

Page: 373

View: 5337

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.
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Essays in Nonlinear Time Series Econometrics

Author: Niels Haldrup,Mika Meitz,Pentti Saikkonen

Publisher: Oxford University Press

ISBN: 0199679959

Category: Business & Economics

Page: 352

View: 7352

This edited collection concerns nonlinear economic relations that involve time. It is divided into four broad themes that all reflect the work and methodology of Professor Timo Teräsvirta, one of the leading scholars in the field of nonlinear time series econometrics. The themes are: Testing for linearity and functional form, specification testing and estimation of nonlinear time series models in the form of smooth transition models, model selection and econometric methodology, and finally applications within the area of financial econometrics. All these research fields include contributions that represent state of the art in econometrics such as testing for neglected nonlinearity in neural network models, time-varying GARCH and smooth transition models, STAR models and common factors in volatility modeling, semi-automatic general to specific model selection for nonlinear dynamic models, high-dimensional data analysis for parametric and semi-parametric regression models with dependent data, commodity price modeling, financial analysts earnings forecasts based on asymmetric loss function, local Gaussian correlation and dependence for asymmetric return dependence, and the use of bootstrap aggregation to improve forecast accuracy. Each chapter represents original scholarly work, and reflects the intellectual impact that Timo Teräsvirta has had and will continue to have, on the profession.
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Nonlinear Time Series Analysis with R

Author: Ray Huffaker,Marco Bittelli,Rodolfo Rosa

Publisher: Oxford University Press

ISBN: 0198782934

Category: Mathematics

Page: 312

View: 4168

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.
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Nonlinear Time Series Analysis

Methods and Applications

Author: Cees Diks

Publisher: World Scientific

ISBN: 9814496006

Category: Science

Page: 220

View: 1189

Methods of nonlinear time series analysis are discussed from a dynamical systems perspective on the one hand, and from a statistical perspective on the other. After giving an informal overview of the theory of dynamical systems relevant to the analysis of deterministic time series, time series generated by nonlinear stochastic systems and spatio-temporal dynamical systems are considered. Several statistical methods for the analysis of nonlinear time series are presented and illustrated with applications to physical and physiological time series. Contents: Nonlinear Dynamical SystemsStochastic Time SeriesA Test for ReversibilityDetecting Differences between Reconstruction MeasuresEstimating Invariants of Noisy AttractorsThe Correlation Integral of Noisy AttractorsSpiral Wave Tip DynamicsSpatio-Temporal Chaos: A Solvable Model Readership: Students and researchers with an interest in time series analysis. Keywords: