Nonlinear Time Series Analysis with R 1st Edition by Ray Huffaker, Marco Bittelli, Rodolfo Rosa ISBN 9780191085796 0191085790

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Product details:
ISBN 10: 0191085790
ISBN 13: 9780191085796
Author: Ray Huffaker, Marco Bittelli, Rodolfo Rosa

Nonlinear Time Series Analysis with R 1st Edition Table of contents:

1 Why Study Nonlinear Time Series Analysis?

1.1 Introduction

1.2 Nonlinear Dynamics and a Strategy for Applying NLTS

1.3 The Contribution of NLTS Diagnostics to Theoretical Modelling

1.4 Caveats in Application

1.5 Summary

2 Linear and Nonlinear Dynamic Behaviour

2.1 Introduction

2.2 Discrete Linear Dynamics

2.3 The Nonlinear Logistic Map

2.4 Stability of Fixed Points

2.5 Dynamics of the Logistic Map

2.6 Analyzing Period Doubling with Bifurcation Diagrams

2.7 Chaotic Behaviour

2.8 Statistical Description of Chaotic Dynamics

2.9 Summary

3 Phase Space Reconstruction

3.1 Introduction

3.2 Ideal Simple Pendulum

3.3 Embedding Procedure

3.4 Phase Space Reconstruction with R packages

3.5 Summary

4 The Features of Chaos

4.1 Introduction

4.2 Lyapunov Exponent

4.3 Recurrence Plots

4.4 Correlation Dimension

4.5 Poincaré Map

4.6 Summary

5 Entropy and Surrogate Testing

5.1 Introduction

5.2 Shannon Entropy of the Logistic Map

5.3 Entropy Test

5.4 Surrogate Test

5.5 Tests for Nonlinear Serial Dependence with R Packages

5.6 Summary

6 Data Preprocessing

6.1 Introduction

6.2 Regular Behaviour of Linear ODE Models

6.3 Noisy Linear Dynamics

6.4 Singular Spectrum Analysis

6.5 Nonstationary Dynamics

6.6 Testing for Nonstationarity in Time Series Data

6.7 Endogenous Complexity with Nonlinear Dynamics

6.8 Summary

7 Surrogate Data Testing

7.1 Introduction

7.2 Surrogate Data Testing in a Nutshell

7.3 Surrogate Types

7.4 Discriminating Statistics

7.5 Rank Order Statistics

7.6 R Code for Surrogate Data Testing

7.7 Summary

8 Empirically Detecting Causality

8.1 Introduction

8.2 Convergent Cross Mapping with R

8.3 Extended (Delayed) Cross Convergent Mapping

8.4 Network Plots

8.5 Real-World Application

8.6 Detecting Change Points

8.7 Detecting Tipping Points

8.8 Summary

9 Phenomenological Modelling

9.1 Introduction

9.2 Components of a Phenomenological Model

9.3 Approximation of Derivatives with Finite Differences

9.4 Multivariate Polynomial Expansions

9.5 Estimating System Coefficients: Ordinary Least Squares

9.6 Estimating System Coefficients: Regularized Regression Methods

9.7 Goodness of Fit

9.8 Solution of Phenomenological Model

9.9 Phenomenological Model Extracted from Three Observed Variables

9.10 Phenomenological Model Extracted from a Single Observed Variable

9.11 Summary

10 Capstone: Application of NLTS to Real-World Data

10.1 Data Preprocessing

10.2 Phase Space Reconstruction

10.3 Surrogate Data Testing

10.4 Convergent Cross Mapping

10.5 Phenomenological Model

10.6 Summary

11 Extreme Value Statistics

11.1 Introduction

11.2 The Generalized Pareto Distribution

11.3 Extreme Value Statistics with R

Appendix A

A.1 Probability Density for the Logistic Map

A.2 Elements of Ergodic Theory

A.3 Dirac Delta Function

Appendix B

B.1 Introduction to the Bootstrap

B.2 Bootstrap Standard Error

B.3 Bootstrapping in R

B.4 Comments

Appendix C

C.1 Properties of Square Matrices

C.2 Analytical Construction of a Phase Diagram

List of Symbols

List of R Codes

References

Index

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Ray Huffaker,Marco Bittelli,Rodolfo Rosa,Nonlinear Time,Analysis,R