Nonlinear Time Series Analysis

Ruey S. Tsay, Rong Chen

• Publisher: Wiley
• Year: 2018
• Print ISBN: 9781119264057
• eBook ISBN: 9781119264071
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: 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. 

CHAPTER 1
Why Should We Care About Nonlinearity?

Linear processes and linear models dominate research and applications of time series analysis. They are often adequate in making statistical inference in practice. Why should we care about nonlinearity then? This is the first question that came to our minds when we thought about writing this book. After all, linear models are easier to use and can provide good approximations in many applications. Empirical time series, on the other hand, are likely to be nonlinear. As such, nonlinear models can certainly make significant contributions, at least in some applications. The goal of this book is to introduce some nonlinear time series models, to discuss situations under which nonlinear models can make contributions, to demonstrate the value and power of nonlinear time series analysis, and to explore the nonlinear world. In many applications, the observed time series are indirect (possibly multidimensional) observations of an unobservable underlying dynamic process that is nonlinear. In this book we also discuss approaches of using nonlinear and non-Gaussian state space models for analyzing such data.

To achieve our objectives, we focus on certain classes of nonlinear time series models that, in our view, are widely applicable and easy to understand. It is not our intention to cover all nonlinear models available in the literature. Readers are referred to Tong (1990), Fan and Yao (2003), Douc et al. (2014), and De Gooijer (2017) for other nonlinear time series models. The book, thus, shows our preference in exploring the nonlinear world. Efforts are made throughout the book to keep applications in mind so that real examples are used whenever possible. We also provide the theory and justifications for the methods and models considered in the book so that readers can have a comprehensive treatment of nonlinear time series analysis. As always, we start with simple models and gradually move toward more complicated ones.

1.1 Some Basic Concepts

A scalar process x_t is a discrete-time time series if x_t is a random variable and the time index t is countable. Typically, we assume the time index t is equally ...

Table of contents

• Cover Page
• Title Page
• Copyright
• Dedication
• Preface
• Chapter 1: Why Should We Care About Nonlinearity?
• Chapter 2: Univariate Parametric Nonlinear Models
• Chapter 3: Univariate Nonparametric Models
• Chapter 4: Neural Networks, Deep Learning, and Tree-based Methods
• Chapter 5: Analysis of Non-Gaussian Time Series
• Chapter 6: State Space Models
• Chapter 7: Nonlinear State Space Models
• Chapter 8: Sequential Monte Carlo
• Index
• EULA