Nonlinear time series analysis with R / Ray Huffaker, Marco Bittelli, Rodolfo Rosa.

Format:

Book

Author/Creator:

Huffaker, Ray G. (Ray Goul), author.

Bittelli, Marco, author.

Rosa, Rodolfo, author.

Language:

English

Subjects (All):

Time-series analysis.

Nonlinear theories.

R (Computer program language).

Physical Description:

ix, 360 pages : illustrations ; 25 cm

Place of Publication:

Oxford ; New York : Oxford University Press 2017.

Summary:

Nonlinear Time Series Analysis with R provides a practical guide to emerging empirical techniques allowing practitioners to diagnose whether highly fluctuating and randomly 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 at 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 competent 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. 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. Book jacket.

Contents:

1 Why Study Nonlinear Time Series Analysis? 1

1.1 Introduction 1

1.2 Nonlinear Dynamics and a Strategy for Applying NLTS 4

1.3 The Contribution of NLTS Diagnostics to Theoretical Modelling 8

1.4 Caveats in Application 8

1.5 Summary 9

2 Linear and Nonlinear Dynamic Behaviour 10

2.1 Introduction 10

2.2 Discrete Linear Dynamics 10

2.3 The Nonlinear Logistic Map 14

2.4 Stability of Fixed Points 17

2.5 Dynamics of the Logistic Map 19

2.6 Analyzing Period Doubling with Bifurcation Diagrams 25

2.7 Chaotic Behaviour 32

2.8 Statistical Description of Chaotic Dynamics 43

2.9 Summary 49

3 Phase Space Reconstruction 51

3.1 Introduction 51

3.2 Ideal Simple Pendulum 52

3.3 Embedding Procedure 57

3.4 Phase Space Reconstruction with R packages 61

3.5 Summary 81

4 The Features of Chaos 83

4.1 Introduction 83

4.2 Lyapunov Exponent 84

4.3 Recurrence Plots 90

4.4 Correlation Dimension 102

4.5 Poincaré Map 111

4.6 Summary 121

5 Entropy and Surrogate Testing 123

5.1 Introduction 123

5.2 Shannon Entropy of the Logistic Map 127

5.3 Entropy Test 128

5.4 Surrogate Test 130

5.5 Tests for Nonlinear Serial Dependence with R Packages 132

5.6 Summary 137

6 Data Preprocessing 140

6.1 Introduction 140

6.2 Regular Behaviour of Linear ODE Models 142

6.3 Noisy Linear Dynamics 151

6.4 Singular Spectrum Analysis 154

6.5 Nonstationary Dynamics 174

6.6 Testing for Nonstationarity in Time Series Data 175

6.7 Endogenous Complexity with Nonlinear Dynamics 188

6.8 Summary 190

7 Surrogate Data Testing 192

7.1 Introduction 192

7.2 Surrogate Data Testing in a Nutshell 194

7.3 Surrogate Types 195

7.4 Discriminating Statistics 198

7.5 Rank Order Statistics 210

7.6 R Code for Surrogate Data Testing 211

7.7 Summary 219

8 Empirically Detecting Causality 221

8.1 Introduction 221

8.2 Convergent Cross Mapping with R 222

8.3 Extended (Delayed) Cross Convergent Mapping 230

8.4 Network Plots 239

8.5 Real-World Application 244

8.6 Detecting Change Points 249

8.7 Detecting Tipping Points 258

8.8 Summary 262

9 Phenomenological Modelling 264

9.1 Introduction 264

9.2 Components of a Phenomenological Model 264

9.3 Approximation of Derivatives with Finite Differences 265

9.4 Multivariate Polynomial Expansions 266

9.5 Estimating System Coefficients: Ordinary Least Squares 270

9.6 Estimating System Coefficients: Regularized Regression Methods 273

9.7 Goodness of Fit 276

9.8 Solution of Phenomenological Model 283

9.9 Phenomenological Model Extracted from Three Observed Variables 287

9.10 Phenomenological Model Extracted from a Single Observed Variable 291

9.11 Summary 295

10 Capstone: Application of NLTS to Real-World Data 298

10.1 Data Preprocessing 299

10.2 Phase Space Reconstruction 301

10.3 Surrogate Data Testing 303

10.4 Convergent Cross Mapping 306

10.5 Phenomenological Model 308

10.6 Summary 311

11 Extreme Value Statistics 313

11.1 Introduction 313

11.2 The Generalized Pareto Distribution 313

11.3 Extreme Value Statistics with R 314.

Notes:

Includes bibliographical references and index.

ISBN:

9780198808251

0198808259

0198782934

9780198782933

OCLC:

982092978