Handbook of Time Series Analysis Recent Theoretical Developments and Applications

, by Schelter, Bjö; rn; Winterhalder, Matthias; Timmer, Jens

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ISBN: 9783527406234 | 3527406239
Cover: Hardcover
Copyright: 10/27/2006

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This handbook provides an up-to-date survey of current research topics and applications of time series analysis methods written by leading experts in their fields. It covers recent developments in univariate as well as bivariate and multivariate time series analysis techniques ranging from physics' to life sciences' applications. Each chapter comprises both methodological aspects and applications to real world complex systems, such as the human brain or Earth's climate. Covering an exceptionally broad spectrum of topics, beginners, experts and practitioners who seek to understand the latest developments will profit from this handbook.

Preface

xiii

List of Contributors

1 Handbook of Time Series Analysis: Introduction and Overview

Björn Schelter, Matthias Winterhalder, and Jens Timmer

(4)

2 Nonlinear Analysis of Time Series Data

Henry D.I. Abarbanel and Ulrich Parlitz

(34)

2.1 Introduction

(1)

2.2 Unfolding the Data: Embedding Theorem in Practice

(12)

2.2.1 Choosing T: Average Mutual Information

(5)

2.2.2 Choosing D: False Nearest Neighbors

(5)

2.2.3 Interspike Intervals

(1)

2.3 Where are We?

(1)

2.4 Lyapunov Exponents: Prediction, Classification, and Chaos

(5)

2.5 Predicting

(4)

2.6 Modeling

(5)

2.6.1 Modeling Interspike Intervals

(1)

2.6.2 Modeling the Observed Membrane Voltage Time Series

(4)

2.6.3 ODE Modeling

(1)

2.7 Conclusion

(2)

References

(4)

3 Local and Cluster Weighted Modeling for Time Series Prediction

David Engster and Ulrich Parlitz

(28)

3.1 Introduction

(3)

3.1.1 Time Series Prediction

(1)

3.1.2 Cross Prediction

(1)

3.1.3 Bias, Variance, Overfitting

(1)

3.2 Local Modeling

(11)

3.2.1 Validation

(2)

3.2.2 Local Polynomial Models

(1)

3.2.3 Local Averaging Models

(1)

3.2.4 Locally Linear Models

(1)

3.2.5 Parameters of Local Modeling

(2)

3.2.6 Regularization

(4)

3.2.7 Optimization of Local Models

(1)

3.3 Cluster Weighted Modeling

(5)

3.3.1 The EM Algorithm

(3)

3.4 Examples

(5)

3.4.1 Noise Reduction

(1)

3.4.2 Signal Through Chaotic Channel

(2)

3.4.3 Friction Modeling

(3)

3.5 Conclusion

(1)

References

(3)

4 Deterministic and Probabilistic Forecasting in Reconstructed State Spaces

Holger Kantz and Eckehard Olbrich

(22)

4.1 Introduction

(2)

4.2 Determinism and Embedding

(6)

4.3 Stochastic Processes

(6)

4.4 Events and Classification Error

(4)

4.5 Conclusions

(1)

References

(3)

5 Dealing with Randomness in Biosignals

Patrick Celka, Rolf Vetter, Elly Gysels, and Trevor J. Hine

(42)

5.1 Introduction

(4)

5.1.1 Determinism: Does It Exist?

(1)

5.1.2 Randomness: An Illusion?

(2)

5.1.3 Randomness and Noise

(1)

5.2 How Do Biological Systems Cope with or Use Randomness?

(3)

5.2.1 Uncertainty Principle in Biology

(1)

5.2.2 Stochastic Resonance in Biology

(2)

5.3 How Do Scientists and Engineers Cope with Randomness and Noise?

(3)

5.4 A Selection of Coping Approaches

(14)

5.4.1 Global State-Space Principal Component Analysis

(10)

5.4.2 Local State-Space Principal Component Analysis

109

(4)

5.5 Applications

113

(13)

5.5.1 Cardiovascular Signals: Observer of the Autonomic Cardiac Modulation

113

(3)

5.5.2 Electroencephalogram: Spontaneous EEG and Evoked Potentials

116

(6)

5.5.3 Speech Enhancement

122

(4)

5.6 Conclusions

126

(1)

References

127

(4)

6 Robust Detail-Preserving Signal Extraction

Ursula Gather, Roland Fried, and Vivian Lanius

131

(28)

6.1 Introduction

131

(3)

6.2 Filters Based on Focal Constant Fits

134

(7)

6.2.1 Standard Median Filters

134

(2)

6.2.2 Modified Order Statistic Filters

136

(2)

6.2.3 Weighted Median Filters

138

(3)

6.3 Filters Based on local linear Fits

141

(4)

6.3.1 Filters Based on Robust Regression

141

(2)

6.3.2 Modified Repeated Median Filters

143

(1)

6.3.3 Weighted Repeated Median Filters

144

(1)

6.4 Modifications for Better Preservation of Shifts

145

(7)

6.4.1 Linear Median Hybrid Filters

145

(2)

6.4.2 Repeated Median Hybrid Filters

147

(2)

6.4.3 Level Shift Detection

149

(2)

6.4.4 Impulse Detection

151

(1)

6.5 Conclusion

152

(1)

References

153

(6)

7 Coupled Oscillators Approach in Analysis of Bivariate Data

Michael Rosenblum, Laura Cimponeriu, and Arkady Pikovsky

159

(22)

7.1 Bivariate Data Analysis: Model-Based Versus Nonmodel-Based Approach

159

(8)

7.1.1 Coupled Oscillators: Main Effects

161

(2)

7.1.2 Weakly Coupled Oscillators: Phase Dynamics Description

163

(1)

7.1.3 Estimation of Phases from Data

164

(2)

7.1.4 Example: Cardiorespiratory Interaction in a Healthy Baby

166

(1)

7.2 Reconstruction of Phase Dynamics from Data

167

(4)

7.3 Characterization of Coupling from Data

171

(6)

7.3.1 Interaction Strength

171

(2)

7.3.2 Directionality of Coupling

173

(2)

7.3.3 Delay in Coupling from Data

175

(2)

7.4 Conclusions and Discussion

177

(1)

References

178

(3)

8 Nonlinear Dynamical Models from Chaotic Time Series: Methods and Applications

Dmitry A. Smirnov and Boris P. Bezruchko

181

(32)

8.1 Introduction

181

(1)

8.2 Scheme of the Modeling Process

182

(2)

8.3 "White Box" Problems

184

(7)

8.3.1 Parameter Estimates and Their Accuracy

184

(4)

8.3.2 Hidden Variables

188

(2)

8.3.3 What Do We Get from Successful and Unsuccessful Modeling Attempts?

190

(1)

8.4 "Gray Box" Problems

191

(4)

8.4.1 Approximation and "Overlearning" Problem

191

(2)

8.4.2 Model Structure Selection

193

(1)

8.4.3 Reconstruction of Regularly Driven Systems

194

(1)

8.5 "Black Box" Problems

195

(4)

8.5.1 Universal Structures of Model Equations

195

(3)

8.5.2 Choice of Dynamical Variables

198

(1)

8.6 Applications of Empirical Models

199

(7)

8.6.1 Method to Reveal Weak Directional Coupling Between Oscillatory Systems from Short Time Series

200

(1)

8.6.2 Application to Climatic Data

201

(2)

8.6.3 Application to Electroencephalogram Data

203

(2)

8.6.4 Other Applications

205

(1)

8.7 Conclusions

206

(1)

References

207

(6)

9 Data-Driven Analysis of Nonstationary Brain Signals

Mario Chavez, Claude Adam, Stefano Boccaletti and Jacques Martinerie

213

(18)

9.1 Introduction

213

(2)

9.1.1 EMD-Related Work

214

(1)

9.2 Intrinsic Time-Scale Decomposition

215

(4)

9.2.1 EMD and Instantaneous Phase Estimation

216

(2)

9.2.2 Drawbacks of the EMD

218

(1)

9.3 Intrinsic Time Scales of Forced Systems

219

(1)

9.4 Intrinsic Time Scales of Coupled Systems

220

(2)

9.5 Intrinsic Time Scales of Epileptic Signals

222

(3)

9.5.1 Intracerebral Activities

222

(1)

9.5.2 Magnetoencephalographic Data

223

(2)

9.6 Time-Scale Synchronization of SEEG Data

225

(1)

9.7 Conclusions

226

(1)

References

227

(4)

10 Synchronization Analysis and Recurrence in Complex Systems

Maria Carmen Romano, Marco Thiel, Jürgen Kurths, Martin Rolfs, Ralf Engbert, and Reinhold Kliegl

231

(34)

10.1 Introduction

231

(2)

10.2 Phase Synchronization by Means of Recurrences

233

(10)

10.2.1 Examples of Application

238

(4)

10.2.2 Influence of Noise

242

(1)

10.3 Generalized Synchronization and Recurrence

243

(6)

10.3.1 Examples of Application

246

(3)

10.4 Transitions to Synchronization

249

(3)

10.5 Twin Surrogates to Test for PS

252

(3)

10.6 Application to Fixational Eye Movements

255

(5)

10.7 Conclusions

260

(1)

References

260

(5)

11 Detecting Coupling in the Presence of Noise and Nonlinearity

Theoden I. Netoff, Thomas L. Carroll, Louis M. Pecora, and Steven J. Schiff

265

(18)

11.1 Introduction

265

(1)

11.2 Methods of Detecting Coupling

266

(4)

11.2.1 Cross-Correlation

266

(1)

11.2.2 Mutual Information

267

(1)

11.2.3 Mutal Information in Two Dimensions

268

(1)

11.2.4 Phase Correlation

268

(1)

11.2.5 Continuity Measure

269

(1)

11.3 Linear and Nonlinear Systems

270

(3)

11.3.1 Gaussian Distributed White Noise

270

(1)

11.3.2 Autoregressive Model

270

(2)

11.3.3 Hénon Map

272

(1)

11.3.4 Rössler Attractor

272

(1)

11.3.5 Circuit Data

273

(1)

11.4 Uncoupled Systems

273

(4)

11.4.1 Correlation Between Gaussian Distributed Random Data Sets

274

(1)

11.4.2 Correlation Between Uncoupled AR Models

274

(1)

11.4.3 Correlation Between Uncoupled Hénon Maps

275

(1)

11.4.4 Correlation Between Uncoupled Rössler Attractors

275

(1)

11.4.5 Uncoupled Electrical Systems

275

(2)

11.5 Weakly Coupled Systems

277

(1)

11.5.1 Coupled AR Models

277

(1)

11.5.2 Coupled Hénon Maps

277

(1)

11.5.3 Weakly Coupled Rössler Attractors

277

(1)

11.5.4 Experimental Electrical Nonlinear Coupled Circuit

278

(1)

11.6 Conclusions

278

(2)

11.7 Discussion

280

(1)

References

281

(2)

12 Linear Models for Mutivariate Time Series

Manfred Deistler

283

(26)

12.1 Introduction

283

(1)

12.2 Stationary Processes and Linear Systems

284

(4)

12.3 Multivariable State Space and ARMA(X) Models

288

(11)

12.3.1 State Space and ARMA(X) Systems

289

(2)

12.3.2 Realization of State Space and ARMA Systems

291

(2)

12.3.3 Parametrization and Semi-Nonparametric Identification

293

(2)

12.3.4 CCA-Subspace Estimators

295

(2)

12.3.5 Maximum Likelihood Estimation Using Data Driven Local Coordinates

297

(2)

12.4 Factor Models for Time Series

299

(5)

12.4.1 Principal Component Analysis

300

(1)

12.4.2 Factor Models with Idiosyncratic Noise

301

(2)

12.4.3 Generalized Linear Dynamic Factor Models

303

(1)

12.5 Summary and Outlook

304

(2)

References

306

(3)

13 Spatio-Temporal Modeling for Biosurveillance

David S. Stoffer and Myron J. Katzoff

309

(26)

13.1 Introduction

309

(1)

13.2 Background

310

(2)

13.3 The State Space Model

312

(4)

13.4 Spatially Constrained Models

316

(4)

13.5 Data Analysis

320

(11)

13.6 Discussion

331

(2)

References

333

(2)

14 Graphical Modeling of Dynamic Relationships in Multivariate Time Series

Michael Eichler

335

(38)

14.1 Introduction

335

(2)

14.2 Granger Causality in Multivariate Time Series

337

(5)

14.2.1 Granger Causality and Vector Autoregressions

337

(3)

14.2.2 Granger Causality in the Frequency Domain

340

(1)

14.2.3 Bivariate Granger Causality

341

(1)

14.3 Graphical Representations of Granger Causality

342

(4)

14.3.1 Path Diagrams for Multivariate Time Series

342

(2)

14.3.2 Bivariate Granger Causality Graphs

344

(2)

14.4 Markov Interpretation of Path Diagrams

346

(8)

14.4.1 Separation in Graphs and the Global Markov Property

346

(2)

14.4.2 The Global Granger-Causal Markov Property

348

(3)

14.4.3 Markov Properties for Bivariate Path Diagrams

351

(1)

14.4.4 Comparison of Bivariate and Multivariate Granger Causality

352

(2)

14.5 Statistical Inference

354

(3)

14.5.1 Inference in the Time Domain

354

(1)

14.5.2 Inference in the Frequency Domain

355

(1)

14.5.3 Graphical Modeling

356

(1)

14.6 Applications

357

(10)

14.6.1 Frequency-Domain Analysis of Multivariate Time Series

358

(5)

14.6.2 Identification of Tremor-Related Pathways

363

(2)

14.6.3 Causal Inference

365

(2)

14.7 Conclusion

367

(1)

References

368

(5)

15 Multivariate Signal Analysis by Parametric Models

Katarzyna J. Blinowksa and Maciej Kaminski

373

(38)

15.1 Introduction

374

(1)

15.2 Parametric Modeling

374

(2)

15.3 Linear Models

376

(1)

15.4 Model Estimation

377

(2)

15.5 Cross Measures

379

(1)

15.6 Causal Estimators

380

(2)

15.7 Modeling of Dynamic Processes

382

(2)

15.8 Simulations

384

(10)

15.8.1 Common Source in Three Channels System

384

(1)

15.8.2 Activity Sink in Five Channels System

384

(4)

15.8.3 Cascade Flows

388

(4)

15.8.4 Comparison between DTF and PDC

392

(2)

15.9 Multivariate Analysis of Experimental Data

394

(9)

15.9.1 Human Sleep Data

394

(6)

15.9.2 Application of a Time-Varying Estimator of Directedness

400

(3)

15.10 Discussion

403

(3)

15.11 Acknowledgements

406

(1)

References

406

(5)

16 Computer Intensive Testing for the Influence Between Time Series

Luiz A. Baccalá, Daniel Y. Takahashi, and Koichi Sameshima

411

(26)

16.1 Introduction

411

(3)

16.2 Basic Resampling Concepts

414

(1)

16.3 Time Series Resampling

415

(5)

16.3.1 Residue Resampling

417

(1)

16.3.2 Phase Resampling

418

(2)

16.3.3 Other Resampling Methods

420

(1)

16.4 Numerical Examples and Applications

420

(11)

16.4.1 Simulated Data

420

(6)

16.4.2 Real Data

426

(5)

16.5 Discussion

431

(2)

16.6 Conclusions

433

(1)

References

433

(4)

17 Granger Causality: Basic Theory and Application to Neuroscience

Mingzhou Ding, Yonghong Chen, and Steven L. Bressler

437

(24)

17.1 Introduction

437

(1)

17.2 Bivariate Time Series and Pairwise Granger Causality

438

(5)

17.2.1 Time Domain Formulation

438

(2)

17.2.2 Frequency Domain Formulation

440

(3)

17.3 Trivariate Time Series and Conditional Granger Causality

443

(4)

17.3.1 Time Domain Formulation

444

(1)

17.3.2 Frequency Domain Formulation

445

(2)

17.4 Estimation of Autoregressive Models

447

(2)

17.5 Numerical Examples

449

(5)

17.5.1 Example 1

449

(2)

17.5.2 Example 2

451

(1)

17.5.3 Example 3

452

(2)

17.6 Analysis of a Beta Oscillation Network in Sensorimotor Cortex

454

(5)

17.7 Summary

459

(1)

References

459

(2)

18 Granger Causality on Spatial Manifolds: Applications to Neuroimaging

Pedro A. Valdés-Sosa, Jose Miguel Bornot-Sánchez, Mayrim Vega-Hernández, Lester Melie-Garcia, Agustin Lage-Castellanos, and Erick Canales-Rodriguez

461

(32)

18.1 Introduction

462

(2)

18.2 The Continuous Spatial Multivariate Autoregressive Model and its Discretization

464

(2)

18.3 Testing for Spatial Granger Causality

466

(2)

18.4 Dimension Reduction Approaches to sMAR Models

468

(3)

18.4.1 ROI-Based Causality Analysis

468

(1)

18.4.2 Latent Variable-Based Causality Analysis

469

(2)

18.5 Penalized sMAR

471

(7)

18.5.1 General Model

471

(3)

18.5.2 Achieving Sparsity Via Variable Selection

474

(2)

18.5.3 Achieving Spatial Smoothness

476

(1)

18.5.4 Achieving Sparseness and Smoothness

477

(1)

18.6 Estimation via the MM Algorithm

478

(3)

18.7 Evaluation of Simulated Data

481

(1)

18.8 Influence Fields for Real Data

482

(3)

18.9 Possible Extensions and Conclusions

485

(1)

References

485

(8)

Index

493

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Handbook of Time Series Analysis Recent Theoretical Developments and Applications

Summary

Author Biography

Table of Contents

Supplemental Materials

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Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Handbook of Time Series Analysis Recent Theoretical Developments and Applications

Summary

Author Biography

Table of Contents

Supplemental Materials

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