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.

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.

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.

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.

Streamflow forecasting is of great importance to water resources management and flood defense. On the other hand, a better understanding of the streamflow process is fundamental for improving the skill of streamflow forecasting. The methods for forecasting streamflows may fall into two general classes: process-driven methods and data-driven methods. Equivalently, methods for understanding streamflow processes may also be broken into two categories: physically-based methods and mathematically-based methods. This thesis focuses on using mathematically-based methods to analyze stochasticity and nonlinearity of streamflow processes based on univariate historic streamflow records, and presents data-driven models that are also mainly based on univariate streamflow time series. Six streamflow processes of five rivers in different geological regions are investigated for stochasticity and nonlinearity at several characteristic timescales.

Nonlinear models have been used extensively in the areas of economics and finance. Recent literature on the topic has shown that a large number of series exhibit nonlinear dynamics as opposed to the alternative--linear dynamics. Incorporating these concepts involves deriving and estimating nonlinear time series models, and these have typically taken the form of Threshold Autoregression (TAR) models, Exponential Smooth Transition (ESTAR) models, and Markov Switching (MS) models, among several others. This edited volume provides a timely overview of nonlinear estimation techniques, offering new methods and insights into nonlinear time series analysis. It features cutting-edge research from leading academics in economics, finance, and business management, and will focus on such topics as Zero-Information-Limit-Conditions, using Markov Switching Models to analyze economics series, and how best to distinguish between competing nonlinear models. Principles and techniques in this book will appeal to econometricians, finance professors teaching quantitative finance, researchers, and graduate students interested in learning how to apply advances in nonlinear time series modeling to solve complex problems in economics and finance.

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.