Nonlinear Time Series Analysis with R 1st edition by Ray Huffaker, Marco Bittelli, Rodolfo Rosa – Ebook PDF Instant Download/Delivery: 0198808259, 9780198808251
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ISBN 10: 0198808259
ISBN 13: 9780198808251
Author: Ray Huffaker, Marco Bittelli, Rodolfo Rosa
Nonlinear Time Series Analysis with R provides a practical guide to emerging empirical techniques allowing practitioners to diagnose whether highly fluctuating and random appearing data are most likely driven by random or deterministic dynamic forces. It joins the chorus of voices recommending ‘getting to know your data’ as an essential preliminary evidentiary step in modelling. Time series are often highly fluctuating with a random appearance. Observed volatility is commonly attributed to exogenous random shocks to stable real-world systems. However, breakthroughs in nonlinear dynamics raise another possibility: highly complex dynamics can emerge endogenously from astoundingly parsimonious deterministic nonlinear models. Nonlinear Time Series Analysis (NLTS) is a collection of empirical tools designed to aid practitioners detect whether stochastic or deterministic dynamics most likely drive observed complexity. Practitioners become ‘data detectives’ accumulating hard empirical evidence supporting their modelling approach. This book is targeted to professionals and graduate students in engineering and the biophysical and social sciences. Its major objectives are to help non-mathematicians — with limited knowledge of nonlinear dynamics — to become operational in NLTS; and in this way to pave the way for NLTS to be adopted in the conventional empirical toolbox and core coursework of the targeted disciplines. Consistent with modern trends in university instruction, the book makes readers active learners with hands-on computer experiments in R code directing them through NLTS methods and helping them understand the underlying logic (please see www.marco.bittelli.com). The computer code is explained in detail so that readers can adjust it for use in their own work. The book also provides readers with an explicit framework — condensed from sound empirical practices recommended in the literature — that details a step-by-step procedure for applying NLTS in real-world data diagnostics.
Nonlinear Time Series Analysis with R 1st 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
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