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Nonlinear time series analysis

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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  Read more...

Abstract: 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.'

Author(s): Chen, Rong; Tsay, Ruey S
Publisher: John Wiley & Sons
Year: 2019

Language: English
Pages: 510
Tags: Time-series analysis.;Nonlinear theories.;MATHEMATICS -- Applied.;MATHEMATICS -- Probability & Statistics -- General.

Content: Intro
Nonlinear Time Series Analysis
Contents
Preface
1 Why Should We Care About Nonlinearity?
1.1 Some Basic Concepts
1.2 Linear Time Series
1.3 Examples of Nonlinear Time Series
1.4 Nonlinearity Tests
1.4.1 Nonparametric Tests
1.4.2 Parametric Tests
Exercises
References
2 Univariate Parametric Nonlinear Models
2.1 A General Formulation
2.1.1 Probability Structure
2.2 Threshold Autoregressive Models
2.2.1 A Two-regime TAR Model
2.2.2 Properties of Two-regime TAR(1) Models
2.2.3 Multiple-regime TAR Models
2.2.4 Estimation of TAR Models
2.2.5 TAR Modeling
2.2.6 Examples. 2.2.7 Predictions of TAR Models2.3 Markov Switching Models
2.3.1 Properties of Markov Switching Models
2.3.2 Statistical Inference of the State Variable
2.3.3 Estimation of Markov Switching Models
2.3.4 Selecting the Number of States
2.3.5 Prediction of Markov Switching Models
2.3.6 Examples
2.4 Smooth Transition Autoregressive Models
2.5 Time-varying Coefficient Models
2.5.1 Functional Coefficient AR Models
2.5.2 Time-varying Coefficient AR Models
2.6 Appendix: Markov Chains
Exercises
References
3 Univariate Nonparametric Models
3.1 Kernel Smoothing
3.2 Local Conditional Mean. 3.3 Local Polynomial Fitting3.4 Splines
3.4.1 Cubic and B-Splines
3.4.2 Smoothing Splines
3.5 Wavelet Smoothing
3.5.1 Wavelets
3.5.2 The Wavelet Transform
3.5.3 Thresholding and Smoothing
3.6 Nonlinear Additive Models
3.7 Index Model and Sliced Inverse Regression
Exercises
References
4 Neural Networks, Deep Learning, and Tree-based Methods
4.1 Neural Networks
4.1.1 Estimation or Training of Neural Networks
4.1.2 An Example
4.2 Deep Learning
4.2.1 Deep Belief Nets
4.2.2 Demonstration
4.3 Tree-based Methods
4.3.1 Decision Trees
4.3.2 Random Forests
Exercises
References. 5 Analysis of Non-Gaussian Time Series5.1 Generalized Linear Time Series Models
5.1.1 Count Data and GLARMA Models
5.2 Autoregressive Conditional Mean Models
5.3 Martingalized GARMA Models
5.4 Volatility Models
5.5 Functional Time Series
5.5.1 Convolution FAR models
5.5.2 Estimation of CFAR Models
5.5.3 Fitted Values and Approximate Residuals
5.5.4 Prediction
5.5.5 Asymptotic Properties
5.5.6 Application
Appendix: Discrete Distributions for Count Data
Exercises
References
6 State Space Models
6.1 A General Model and Statistical Inference
6.2 Selected Examples. 6.2.1 Linear Time Series Models6.2.2 Time Series With Observational Noises
6.2.3 Time-varying Coefficient Models
6.2.4 Target Tracking
6.2.5 Signal Processing in Communications
6.2.6 Dynamic Factor Models
6.2.7 Functional and Distributional Time Series
6.2.8 Markov Regime Switching Models
6.2.9 Stochastic Volatility Models
6.2.10 Non-Gaussian Time Series
6.2.11 Mixed Frequency Models
6.2.12 Other Applications
6.3 Linear Gaussian State Space Models
6.3.1 Filtering and the Kalman Filter
6.3.2 Evaluating the likelihood function
6.3.3 Smoothing
6.3.4 Prediction and Missing Data.