Nonlinear Time Series Analysis 1st Edition by Ruey S. Tsay, Rong Chen – Ebook PDF Instant Download/Delivery: 1119264057, 9781119264057
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ISBN 10: 1119264057
ISBN 13: 9781119264057
Author: Ruey S. Tsay, Rong Chen
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.
Nonlinear Time Series Analysis 1st Table of contents:
Chapter 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
1.5 Exercises
References
Chapter 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 Models
2.3 Markov Switching Models
2.3.1 Properties of Markov Switching Models
2.3.2 Statistical Inference of the State Variable
2.3.2.1 Filtering State Probabilities
2.3.2.2 Smoothing State Probabilities
2.3.3 Estimation of Markov Switching Models
2.3.3.1 The States are Known
2.3.3.2 The States are Unknown
2.3.3.3 Sampling the Unknown Transition Matrix
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
2.7 Exercises
References
Chapter 3: Univariate Nonparametric Models
3.1 Kernel Smoothing
3.2 Local Conditional Mean
3.3 Local Polynomial Fitting
3.4 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
3.8 Exercises
References
Chapter 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
4.3.1.1 Regression Tree
4.3.1.2 Tree Pruning
4.3.1.3 Classification Tree
4.3.1.4 Bagging
4.3.2 Random Forests
4.4 Exercises
References
Chapter 5: Analysis of Non-Gaussian Time Series
5.1 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
5.6 Appendix: Discrete Distributions for Count Data
5.7 Exercises
References
Chapter 6: State Space Models
6.1 A General Model and Statistical Inference
6.2 Selected Examples
6.2.1 Linear Time Series Models
6.2.2 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
6.3.5 Sequential Processing
6.3.6 Examples and R Demonstrations
6.4 Exercises
References
Chapter 7: Nonlinear State Space Models
7.1 Linear and Gaussian Approximations
7.1.1 Kalman Filter for Linear Non-Gaussian Systems
7.1.2 Extended Kalman Filters for Nonlinear Systems
7.1.3 Gaussian Sum Filters
7.1.4 The Unscented Kalman Filter
7.1.5 Ensemble Kalman Filters
7.1.6 Examples and R implementations
7.2 Hidden Markov Models
7.2.1 Filtering
7.2.2 Smoothing
7.2.3 The Most Likely State Path: the Viterbi Algorithm
7.2.4 Parameter Estimation: the Baum–Welch Algorithm
7.2.5 HMM Examples and R Implementation
7.3 Exercises
References
Chapter 8: Sequential Monte Carlo
8.1 A Brief Overview of Monte Carlo Methods
8.1.1 General Methods of Generating Random Samples
8.1.2 Variance Reduction Methods
8.1.3 Importance Sampling
8.1.4 Markov Chain Monte Carlo
8.2 The SMC Framework
8.3 Design Issue I: Propagation
8.3.1 Proposal Distributions
8.3.2 Delay Strategy (Lookahead)
8.4 Design Issue II: Resampling
8.4.1 The Priority Score
8.4.2 Choice of Sampling Methods in Resampling
8.4.3 Resampling Schedule
8.4.4 Benefits of Resampling
8.5 Design Issue III: Inference
8.6 Design Issue IV: Marginalization and the Mixture Kalman Filter
8.6.1 Conditional Dynamic Linear Models
8.6.2 Mixture Kalman Filters
8.7 Smoothing with SMC
8.7.1 Simple Weighting Approach
8.7.2 Weight Marginalization Approach
8.7.3 Two-filter Sampling
8.8 Parameter Estimation with SMC
8.8.1 Maximum Likelihood Estimation
8.8.2 Bayesian Parameter Estimation
8.8.3 Varying Parameter Approach
8.9 Implementation Considerations
8.10 Examples and R Implementation
8.10.1 R Implementation of SMC: Generic SMC and Resampling Methods
8.10.1.1 Generic R Code for SMC Implementation
8.10.1.2 R Code for Resampling
8.10.2 Tracking in a Clutter Environment
8.10.3 Bearing-only Tracking with Passive Sonar
8.10.4 Stochastic Volatility Models
8.10.5 Fading Channels as Conditional Dynamic Linear Models
8.11 Exercises
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