Chapter
1.4.1 Nonparametric Tests
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
2.2.7 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
2.3.3 Estimation of Markov Switching Models
2.3.4 Selecting the Number of States
2.3.5 Prediction of Markov Switching Models
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
3 Univariate Nonparametric Models
3.2 Local Conditional Mean
3.3 Local Polynomial Fitting
3.4.1 Cubic and B-Splines
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
4 Neural Networks, Deep Learning, and Tree-based Methods
4.1.1 Estimation or Training of Neural Networks
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
5.5 Functional Time Series
5.5.1 Convolution FAR models
5.5.2 Estimation of CFAR Models
5.5.3 Fitted Values and Approximate Residuals
5.5.5 Asymptotic Properties
Appendix: Discrete Distributions for Count Data
6.1 A General Model and Statistical Inference
6.2.1 Linear Time Series Models
6.2.2 Time Series With Observational Noises
6.2.3 Time-varying Coefficient Models
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
6.3.4 Prediction and Missing Data
6.3.5 Sequential Processing
6.3.6 Examples and R Demonstrations
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
7.2.3 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
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
8.3 Design Issue I: Propagation
8.3.1 Proposal Distributions
8.3.2 Delay Strategy (Lookahead)
8.4 Design Issue II: Resampling
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
8.7.1 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
8.10.2 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
Nonlinear Time Series Analysis
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