Handbook of time series analysis: recent theoretical developments and applications
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| Beschreibung: | XVIII, 496 S. Ill., graph. Darst. 270 mm x 140 mm |
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| 245 | 1 | 0 | |a Handbook of time series analysis |b recent theoretical developments and applications |c ed. by Björn Schelter ... |
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Datensatz im Suchindex
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| adam_text | Contents
Preface xiii
List of Contributors xv
1 Handbook of Time Series Analysis: Introduction and Overview
(Bjorn Schelter, Matthias Winterhalder, and Jens Timmer) 1
2 Nonlinear Analysis of Time Series Data
(Henry D, I. Abarbanel and Ulrich Parlitz) 5
2.1 Introduction 5
2.2 Unfolding the Data: Embedding Theorem in Practice 6
2.2.1 Choosing T: Average Mutual Information 8
2.2.2 Choosing D: False Nearest Neighbors 13
2.2.3 Interspike Intervals 18
2.3 Where are We? 18
2.4 Lyapunov Exponents: Prediction, Classification, and Chaos .... 19
2.5 Predicting 24
2.6 Modeling 28
2.6.1 Modeling Interspike Intervals 28
2.6.2 Modeling the Observed Membrane Voltage Time Series . . 29
2.6.3 ODE Modeling 33
2.7 Conclusion 33
References 35
3 Local and Cluster Weighted Modeling for Time Series Prediction
(David Engster and Ulrich Parlitz) 39
3.1 Introduction 39
3.1.1 Time Series Prediction 40
3.1.2 Cross Prediction 40
3.1.3 Bias, Variance, Overfitting 41
3.2 Local Modeling 42
3.2.1 Validation 43
3.2.2 Local Polynomial Models 45
3.2.3 Local Averaging Models 46
3.2.4 Locally Linear Models 46
3.2.5 Parameters of Local Modeling 46
3.2.6 Regularization 48
3.2.7 Optimization of Local Models 52
Handbook of Time Series Analysis. Bjorn Schelter, Matthias Winterhalder, Jens Timmer
Copyright © 2006 WILEY VCH Verlag GmbH Co. KGaA, Weinheim
ISBN: 3 527 40623 9
vi Contents
3.3 Cluster Weighted Modeling 53
3.3.1 The EM Algorithm 55
3.4 Examples 58
3.4.1 Noise Reduction 58
3.4.2 Signal Through Chaotic Channel 58
3.4.3 Friction Modeling 60
3.5 Conclusion 63
References 64
4 Deterministic and Probabilistic Forecasting in Reconstructed State Spaces
(Holger Kantz and Eckehard Olbrich) 67
4.1 Introduction 67
4.2 Determinism and Embedding 69
4.3 Stochastic Processes 75
4.4 Events and Classification Error 81
4.5 Conclusions 85
References 86
5 Dealing with Randomness in Biosignals
(Patrick Celka, Rolf Vetter, Elly Gysels, and Trevor }. Him) 89
5.1 Introduction 89
5.1.1 Determinism: Does It Exist? 90
5.1.2 Randomness: An Illusion? 90
5.1.3 Randomness and Noise 92
5.2 How Do Biological Systems Cope with or Use Randomness? ... 93
5.2.1 Uncertainty Principle in Biology 93
5.2.2 Stochastic Resonance in Biology 94
5.3 How Do Scientists and Engineers Cope with Randomness
and Noise? 96
5.4 A Selection of Coping Approaches 99
5.4.1 Global State Space Principal Component Analysis 99
5.4.2 Local State Space Principal Component Analysis 109
5.5 Applications 113
5.5.1 Cardiovascular Signals: Observer of the Autonomic
Cardiac Modulation 113
5.5.2 Electroencephalogram: Spontaneous EEG and Evoked
Potentials 116
5.5.3 Speech Enhancement 122
5.6 Conclusions 126
References 127
6 Robust Detail Preserving Signal Extraction
(Ursula Gather, Roland Fried, and Vivian Lanius) 131
6.1 Introduction 131
Contents vii
6.2 Filters Based on Local Constant Fits 134
6.2.1 Standard Median Filters 134
6.2.2 Modified Order Statistic Filters 136
6.2.3 Weighted Median Filters 138
6.3 Filters Based on Local Linear Fits 141
6.3.1 Filters Based on Robust Regression 141
6.3.2 Modified Repeated Median Filters 143
6.3.3 Weighted Repeated Median Filters 144
6.4 Modifications for Better Preservation of Shifts 145
6.4.1 Linear Median Hybrid Filters 145
6.4.2 Repeated Median Hybrid Filters 147
6.4.3 Level Shift Detection 149
6.4.4 Impulse Detection 151
6.5 Conclusions 152
References 153
7 Coupled Oscillators Approach in Analysis of Bivariate Data
(Michael Rosenblum, Laura Cimponeriu, and Arkady Pikovsky) 159
7.1 Bivariate Data Analysis: Model Based Versus Nonmodel Based
Approach 159
7.1.1 Coupled Oscillators: Main Effects 161
7.1.2 Weakly Coupled Oscillators: Phase Dynamics Description . 163
7.1.3 Estimation of Phases from Data 164
7.1.4 Example: Cardiorespiratory Interaction in a Healthy Baby . 166
7.2 Reconstruction of Phase Dynamics from Data 167
7.3 Characterization of Coupling from Data 171
7.3.1 Interaction Strength 171
7.3.2 Directionality of Coupling 173
7.3.3 Delay in Coupling from Data 175
7.4 Conclusions and Discussion 177
References 178
8 Nonlinear Dynamical Models from Chaotic Time Series:
Methods and Applications
{Dmitry A. Smirnov and Boris P. Bezruchko) 181
8.1 Introduction 181
8.2 Scheme of the Modeling Process 182
8.3 White Box Problems 184
8.3.1 Parameter Estimates and Their Accuracy 184
8.3.2 Hidden Variables 188
8.3.3 What Do We Get from Successful and Unsuccessful
Modeling Attempts? 190
8.4 Gray Box Problems 191
8.4.1 Approximation and Overlearning Problem 191
viii Contents
8.4.2 Model Structure Selection 193
8.4.3 Reconstruction of Regularly Driven Systems 194
8.5 Black Box Problems 195
8.5.1 Universal Structures of Model Equations 195
8.5.2 Choice of Dynamical Variables 198
8.6 Applications of Empirical Models 199
8.6.1 Method to Reveal Weak Directional Coupling
Between Oscillatory Systems from Short Time Series .... 200
8.6.2 Application to Climatic Data 201
8.6.3 Application to Electroencephalogram Data 203
8.6.4 Other Applications 205
8.7 Conclusions 206
References 207
9 Data Driven Analysis of Nonstationary Brain Signals
(Mario Chavez, Claude Adam, Stefano Boccaletti and Jacques Martinerie) 213
9.1 Introduction 213
9.1.1 EMD Related Work 214
9.2 Intrinsic Time Scale Decomposition 215
9.2.1 EMD and Instantaneous Phase Estimation 216
9.2.2 Drawbacks of the EMD 218
9.3 Intrinsic Time Scales of Forced Systems 219
9.4 Intrinsic Time Scales of Coupled Systems 220
9.5 Intrinsic Time Scales of Epileptic Signals 222
9.5.1 Intracerebral Activities 222
9.5.2 Magnetoencephalographic Data 223
9.6 Time Scale Synchronization of SEEG Data 225
9.7 Conclusions 226
References 227
10 Synchronization Analysis and Recurrence in Complex Systems
(Maria Carmen Romano, Marco Thiel, Jtirgen Kurths, Martin Rolfs, 231
Ralf Engbert, and Reinhold Kliegl)
10.1 Introduction 231
10.2 Phase Synchronization by Means of Recurrences 233
10.2.1 Examples of Application 238
10.2.2 Influence of Noise 242
10.3 Generalized Synchronization and Recurrence 243
10.3.1 Examples of Application 246
10.4 Transitions to Synchronization 249
10.5 Twin Surrogates to Test for PS 252
10.6 Application to Fixational Eye Movements 255
10.7 Conclusions 260
References 260
Contents ix
11 Detecting Coupling in the Presence of Noise and Nonlinearity
(Theoden I. Netoff, Thomas L. Carroll, Louis M. Pecora, and Steven J. Schiff) 265
11.1 Introduction 265
11.2 Methods of Detecting Coupling 266
11.2.1 Cross Correlation 266
11.2.2 Mutual Information 267
11.2.3 Mutual Information in Two Dimensions 268
11.2.4 Phase Correlation 268
11.2.5 Continuity Measure 269
11.3 Linear and Nonlinear Systems 270
11.3.1 Gaussian Distributed White Noise 270
11.3.2 Autoregressive Model 270
11.3.3 Henon Map 272
11.3.4 Rossler Attractor 272
11.3.5 Circuit Data 273
11.4 Uncoupled Systems 273
11.4.1 Correlation Between Gaussian Distributed Random
Data Sets 274
11.4.2 Correlation Between Uncoupled AR Models 274
11.4.3 Correlation Between Uncoupled Henon Maps 275
11.4.4 Correlation Between Uncoupled Rossler Attractors 275
11.4.5 Uncoupled Electrical Systems 275
11.5 Weakly Coupled Systems 277
11.5.1 Coupled AR Models 277
11.5.2 Coupled Henon Maps 277
11.5.3 Weakly Coupled Rossler Attractors 277
11.5.4 Experimental Electrical Nonlinear Coupled Circuit 278
11.6 Conclusions 278
11.7 Discussion 280
References 281
12 Linear Models for Mutivariate Time Series
{Manfred Deistler) 283
12.1 Introduction 283
12.2 Stationary Processes and Linear Systems 284
12.3 Multivariable State Space and ARMA(X) Models 288
12.3.1 State Space and ARMA(X) Systems 289
12.3.2 Realization of State Space and ARMA Systems 291
12.3.3 Parametrization and Semi Nonparametric Identification . . 293
12.3.4 CCA Subspace Estimators 295
12.3.5 Maximum Likelihood Estimation Using Data Driven Local
Coordinates 297
12.4 Factor Models for Time Series 299
12.4.1 Principal Component Analysis 300
x Contents
12.4.2 Factor Models with Idiosyncratic Noise 301
12.4.3 Generalized Linear Dynamic Factor Models 303
12.5 Summary and Outlook 304
References 306
13 Spatio Temporal Modeling for Biosurveillance
(David S. Stoffer and Myron }. Katzoff) 309
13.1 Introduction 309
13.2 Background 310
13.3 The State Space Model 312
13.4 Spatially Constrained Models 316
13.5 Data Analysis 320
13.6 Discussion 331
References 333
14 Graphical Modeling of Dynamic Relationships
in Multivariate Time Series
(Michael Eichler) 335
14.1 Introduction 335
14.2 Granger Causality in Multivariate Time Series 337
14.2.1 Granger Causality and Vector Autoregressions 337
14.2.2 Granger Causality in the Frequency Domain 340
14.2.3 Bivariate Granger Causality 341
14.3 Graphical Representations of Granger Causality 342
14.3.1 Path Diagrams for Multivariate Time Series 342
14.3.2 Bivariate Granger Causality Graphs 344
14.4 Markov Interpretation of Path Diagrams 346
14.4.1 Separation in Graphs and the Global Markov Property . . . 346
14.4.2 The Global Granger Causal Markov Property 348
14.4.3 Markov Properties for Bivariate Path Diagrams 351
14.4.4 Comparison of Bivariate and Multivariate Granger Causality 352
14.5 Statistical Inference 354
14.5.1 Inference in the Time Domain 354
14.5.2 Inference in the Frequency Domain 355
14.5.3 Graphical Modeling 356
14.6 Applications 357
14.6.1 Frequency Domain Analysis of Multivariate Time Series . . 358
14.6.2 Identification of Tremor Related Pathways 363
14.6.3 Causal Inference 365
14.7 Conclusion 367
References 368
Contents xi
15 Multivariate Signal Analysis by Parametric Models
(Katarzyna ]. Blinowska and Maciej Kaminski) 373
15.1 Introduction 374
15.2 Parametric Modeling 374
15.3 Linear Models 376
15.4 Model Estimation 377
15.5 Cross Measures 379
15.6 Causal Estimators 380
15.7 Modeling of Dynamic Processes 382
15.8 Simulations 384
15.8.1 Common Source in Three Channels System 384
15.8.2 Activity Sink in Five Channels System 384
15.8.3 Cascade Flows 388
15.8.4 Comparison between DTF and PDC 392
15.9 Multivariate Analysis of Experimental Data 394
15.9.1 Human Sleep Data 394
15.9.2 Application of a Time Varying Estimator of Directedness . 400
15.10Discussion 403
15.11Acknowledgements 406
References 406
16 Computer Intensive Testing for the Influence Between Time Series
(Luiz A. Baccald, Daniel Y. Takahashi, and Koichi Sameshima) 411
16.1 Introduction 411
16.2 Basic Resampling Concepts 414
16.3 Time Series Resampling 415
16.3.1 Residue Resampling 417
16.3.2 Phase Resampling 418
16.3.3 Other Resampling Methods 420
16.4 Numerical Examples and Applications 420
16.4.1 Simulated Data 420
16.4.2 Real Data 426
16.5 Discussion 431
16.6 Conclusions 433
References 433
17 Granger Causality: Basic Theory and Application to Neuroscience
(Mingzhou Ding, Yonghong Chen, and Steven L. Bressler) 437
17.1 Introduction 437
17.2 Bivariate Time Series and Pairwise Granger Causality 438
17.2.1 Time Domain Formulation 438
17.2.2 Frequency Domain Formulation 440
17.3 Trivariate Time Series and Conditional Granger Causality 443
17.3.1 Time Domain Formulation 444
xii Contents
17.3.2 Frequency Domain Formulation 445
17.4 Estimation of Autoregressive Models 447
17.5 Numerical Examples 449
17.5.1 Example 1 449
17.5.2 Example 2 451
17.5.3 Example 3 452
17.6 Analysis of a Beta Oscillation Network in Sensorimotor Cortex . . 454
17.7 Summary 459
References 459
18 Granger Causality on Spatial Manifolds:
Applications to Neuroimaging
(Pedro A. ValMs Sosa, Jose Miguel Bornot Sdnchez, Mayrim Vega Hernandez, 461
Lester Melie Garcia, Agustin Lage Castellanos, and Erick Canales Rodriguez)
18.1 Introduction 462
18.2 The Continuous Spatial Multivariate Autoregressive Model
and its Discretization 464
18.3 Testing for Spatial Granger Causality 466
18.4 Dimension Reduction Approaches to sMAR Models 468
18.4.1 ROI Based Causality Analysis 468
18.4.2 Latent Variable Based Causality Analysis 469
18.5 Penalized sMAR 471
18.5.1 General Model 471
18.5.2 Achieving Sparsity Via Variable Selection 474
18.5.3 Achieving Spatial Smoothness 476
18.5.4 Achieving Sparseness and Smoothness 477
18.6 Estimation via the MM Algorithm 478
18.7 Evaluation of Simulated Data 481
18.8 Influence Fields for Real Data 482
18.9 Possible Extensions and Conclusions 485
References 485
Index 493
|
| adam_txt |
Contents
Preface xiii
List of Contributors xv
1 Handbook of Time Series Analysis: Introduction and Overview
(Bjorn Schelter, Matthias Winterhalder, and Jens Timmer) 1
2 Nonlinear Analysis of Time Series Data
(Henry D, I. Abarbanel and Ulrich Parlitz) 5
2.1 Introduction 5
2.2 Unfolding the Data: Embedding Theorem in Practice 6
2.2.1 Choosing T: Average Mutual Information 8
2.2.2 Choosing D: False Nearest Neighbors 13
2.2.3 Interspike Intervals 18
2.3 Where are We? 18
2.4 Lyapunov Exponents: Prediction, Classification, and Chaos . 19
2.5 Predicting 24
2.6 Modeling 28
2.6.1 Modeling Interspike Intervals 28
2.6.2 Modeling the Observed Membrane Voltage Time Series . . 29
2.6.3 ODE Modeling 33
2.7 Conclusion 33
References 35
3 Local and Cluster Weighted Modeling for Time Series Prediction
(David Engster and Ulrich Parlitz) 39
3.1 Introduction 39
3.1.1 Time Series Prediction 40
3.1.2 Cross Prediction 40
3.1.3 Bias, Variance, Overfitting 41
3.2 Local Modeling 42
3.2.1 Validation 43
3.2.2 Local Polynomial Models 45
3.2.3 Local Averaging Models 46
3.2.4 Locally Linear Models 46
3.2.5 Parameters of Local Modeling 46
3.2.6 Regularization 48
3.2.7 Optimization of Local Models 52
Handbook of Time Series Analysis. Bjorn Schelter, Matthias Winterhalder, Jens Timmer
Copyright © 2006 WILEY VCH Verlag GmbH Co. KGaA, Weinheim
ISBN: 3 527 40623 9
vi Contents
3.3 Cluster Weighted Modeling 53
3.3.1 The EM Algorithm 55
3.4 Examples 58
3.4.1 Noise Reduction 58
3.4.2 Signal Through Chaotic Channel 58
3.4.3 Friction Modeling 60
3.5 Conclusion 63
References 64
4 Deterministic and Probabilistic Forecasting in Reconstructed State Spaces
(Holger Kantz and Eckehard Olbrich) 67
4.1 Introduction 67
4.2 Determinism and Embedding 69
4.3 Stochastic Processes 75
4.4 Events and Classification Error 81
4.5 Conclusions 85
References 86
5 Dealing with Randomness in Biosignals
(Patrick Celka, Rolf Vetter, Elly Gysels, and Trevor }. Him) 89
5.1 Introduction 89
5.1.1 Determinism: Does It Exist? 90
5.1.2 Randomness: An Illusion? 90
5.1.3 Randomness and Noise 92
5.2 How Do Biological Systems Cope with or Use Randomness? . 93
5.2.1 Uncertainty Principle in Biology 93
5.2.2 Stochastic Resonance in Biology 94
5.3 How Do Scientists and Engineers Cope with Randomness
and Noise? 96
5.4 A Selection of Coping Approaches 99
5.4.1 Global State Space Principal Component Analysis 99
5.4.2 Local State Space Principal Component Analysis 109
5.5 Applications 113
5.5.1 Cardiovascular Signals: Observer of the Autonomic
Cardiac Modulation 113
5.5.2 Electroencephalogram: Spontaneous EEG and Evoked
Potentials 116
5.5.3 Speech Enhancement 122
5.6 Conclusions 126
References 127
6 Robust Detail Preserving Signal Extraction
(Ursula Gather, Roland Fried, and Vivian Lanius) 131
6.1 Introduction 131
Contents vii
6.2 Filters Based on Local Constant Fits 134
6.2.1 Standard Median Filters 134
6.2.2 Modified Order Statistic Filters 136
6.2.3 Weighted Median Filters 138
6.3 Filters Based on Local Linear Fits 141
6.3.1 Filters Based on Robust Regression 141
6.3.2 Modified Repeated Median Filters 143
6.3.3 Weighted Repeated Median Filters 144
6.4 Modifications for Better Preservation of Shifts 145
6.4.1 Linear Median Hybrid Filters 145
6.4.2 Repeated Median Hybrid Filters 147
6.4.3 Level Shift Detection 149
6.4.4 Impulse Detection 151
6.5 Conclusions 152
References 153
7 Coupled Oscillators Approach in Analysis of Bivariate Data
(Michael Rosenblum, Laura Cimponeriu, and Arkady Pikovsky) 159
7.1 Bivariate Data Analysis: Model Based Versus Nonmodel Based
Approach 159
7.1.1 Coupled Oscillators: Main Effects 161
7.1.2 Weakly Coupled Oscillators: Phase Dynamics Description . 163
7.1.3 Estimation of Phases from Data 164
7.1.4 Example: Cardiorespiratory Interaction in a Healthy Baby . 166
7.2 Reconstruction of Phase Dynamics from Data 167
7.3 Characterization of Coupling from Data 171
7.3.1 Interaction Strength 171
7.3.2 Directionality of Coupling 173
7.3.3 Delay in Coupling from Data 175
7.4 Conclusions and Discussion 177
References 178
8 Nonlinear Dynamical Models from Chaotic Time Series:
Methods and Applications
{Dmitry A. Smirnov and Boris P. Bezruchko) 181
8.1 Introduction 181
8.2 Scheme of the Modeling Process 182
8.3 "White Box" Problems 184
8.3.1 Parameter Estimates and Their Accuracy 184
8.3.2 Hidden Variables 188
8.3.3 What Do We Get from Successful and Unsuccessful
Modeling Attempts? 190
8.4 "Gray Box" Problems 191
8.4.1 Approximation and "Overlearning" Problem 191
viii Contents
8.4.2 Model Structure Selection 193
8.4.3 Reconstruction of Regularly Driven Systems 194
8.5 "Black Box" Problems 195
8.5.1 Universal Structures of Model Equations 195
8.5.2 Choice of Dynamical Variables 198
8.6 Applications of Empirical Models 199
8.6.1 Method to Reveal Weak Directional Coupling
Between Oscillatory Systems from Short Time Series . 200
8.6.2 Application to Climatic Data 201
8.6.3 Application to Electroencephalogram Data 203
8.6.4 Other Applications 205
8.7 Conclusions 206
References 207
9 Data Driven Analysis of Nonstationary Brain Signals
(Mario Chavez, Claude Adam, Stefano Boccaletti and Jacques Martinerie) 213
9.1 Introduction 213
9.1.1 EMD Related Work 214
9.2 Intrinsic Time Scale Decomposition 215
9.2.1 EMD and Instantaneous Phase Estimation 216
9.2.2 Drawbacks of the EMD 218
9.3 Intrinsic Time Scales of Forced Systems 219
9.4 Intrinsic Time Scales of Coupled Systems 220
9.5 Intrinsic Time Scales of Epileptic Signals 222
9.5.1 Intracerebral Activities 222
9.5.2 Magnetoencephalographic Data 223
9.6 Time Scale Synchronization of SEEG Data 225
9.7 Conclusions 226
References 227
10 Synchronization Analysis and Recurrence in Complex Systems
(Maria Carmen Romano, Marco Thiel, Jtirgen Kurths, Martin Rolfs, 231
Ralf Engbert, and Reinhold Kliegl)
10.1 Introduction 231
10.2 Phase Synchronization by Means of Recurrences 233
10.2.1 Examples of Application 238
10.2.2 Influence of Noise 242
10.3 Generalized Synchronization and Recurrence 243
10.3.1 Examples of Application 246
10.4 Transitions to Synchronization 249
10.5 Twin Surrogates to Test for PS 252
10.6 Application to Fixational Eye Movements 255
10.7 Conclusions 260
References 260
Contents ix
11 Detecting Coupling in the Presence of Noise and Nonlinearity
(Theoden I. Netoff, Thomas L. Carroll, Louis M. Pecora, and Steven J. Schiff) 265
11.1 Introduction 265
11.2 Methods of Detecting Coupling 266
11.2.1 Cross Correlation 266
11.2.2 Mutual Information 267
11.2.3 Mutual Information in Two Dimensions 268
11.2.4 Phase Correlation 268
11.2.5 Continuity Measure 269
11.3 Linear and Nonlinear Systems 270
11.3.1 Gaussian Distributed White Noise 270
11.3.2 Autoregressive Model 270
11.3.3 Henon Map 272
11.3.4 Rossler Attractor 272
11.3.5 Circuit Data 273
11.4 Uncoupled Systems 273
11.4.1 Correlation Between Gaussian Distributed Random
Data Sets 274
11.4.2 Correlation Between Uncoupled AR Models 274
11.4.3 Correlation Between Uncoupled Henon Maps 275
11.4.4 Correlation Between Uncoupled Rossler Attractors 275
11.4.5 Uncoupled Electrical Systems 275
11.5 Weakly Coupled Systems 277
11.5.1 Coupled AR Models 277
11.5.2 Coupled Henon Maps 277
11.5.3 Weakly Coupled Rossler Attractors 277
11.5.4 Experimental Electrical Nonlinear Coupled Circuit 278
11.6 Conclusions 278
11.7 Discussion 280
References 281
12 Linear Models for Mutivariate Time Series
{Manfred Deistler) 283
12.1 Introduction 283
12.2 Stationary Processes and Linear Systems 284
12.3 Multivariable State Space and ARMA(X) Models 288
12.3.1 State Space and ARMA(X) Systems 289
12.3.2 Realization of State Space and ARMA Systems 291
12.3.3 Parametrization and Semi Nonparametric Identification . . 293
12.3.4 CCA Subspace Estimators 295
12.3.5 Maximum Likelihood Estimation Using Data Driven Local
Coordinates 297
12.4 Factor Models for Time Series 299
12.4.1 Principal Component Analysis 300
x Contents
12.4.2 Factor Models with Idiosyncratic Noise 301
12.4.3 Generalized Linear Dynamic Factor Models 303
12.5 Summary and Outlook 304
References 306
13 Spatio Temporal Modeling for Biosurveillance
(David S. Stoffer and Myron }. Katzoff) 309
13.1 Introduction 309
13.2 Background 310
13.3 The State Space Model 312
13.4 Spatially Constrained Models 316
13.5 Data Analysis 320
13.6 Discussion 331
References 333
14 Graphical Modeling of Dynamic Relationships
in Multivariate Time Series
(Michael Eichler) 335
14.1 Introduction 335
14.2 Granger Causality in Multivariate Time Series 337
14.2.1 Granger Causality and Vector Autoregressions 337
14.2.2 Granger Causality in the Frequency Domain 340
14.2.3 Bivariate Granger Causality 341
14.3 Graphical Representations of Granger Causality 342
14.3.1 Path Diagrams for Multivariate Time Series 342
14.3.2 Bivariate Granger Causality Graphs 344
14.4 Markov Interpretation of Path Diagrams 346
14.4.1 Separation in Graphs and the Global Markov Property . . . 346
14.4.2 The Global Granger Causal Markov Property 348
14.4.3 Markov Properties for Bivariate Path Diagrams 351
14.4.4 Comparison of Bivariate and Multivariate Granger Causality 352
14.5 Statistical Inference 354
14.5.1 Inference in the Time Domain 354
14.5.2 Inference in the Frequency Domain 355
14.5.3 Graphical Modeling 356
14.6 Applications 357
14.6.1 Frequency Domain Analysis of Multivariate Time Series . . 358
14.6.2 Identification of Tremor Related Pathways 363
14.6.3 Causal Inference 365
14.7 Conclusion 367
References 368
Contents xi
15 Multivariate Signal Analysis by Parametric Models
(Katarzyna ]. Blinowska and Maciej Kaminski) 373
15.1 Introduction 374
15.2 Parametric Modeling 374
15.3 Linear Models 376
15.4 Model Estimation 377
15.5 Cross Measures 379
15.6 Causal Estimators 380
15.7 Modeling of Dynamic Processes 382
15.8 Simulations 384
15.8.1 Common Source in Three Channels System 384
15.8.2 Activity Sink in Five Channels System 384
15.8.3 Cascade Flows 388
15.8.4 Comparison between DTF and PDC 392
15.9 Multivariate Analysis of Experimental Data 394
15.9.1 Human Sleep Data 394
15.9.2 Application of a Time Varying Estimator of Directedness . 400
15.10Discussion 403
15.11Acknowledgements 406
References 406
16 Computer Intensive Testing for the Influence Between Time Series
(Luiz A. Baccald, Daniel Y. Takahashi, and Koichi Sameshima) 411
16.1 Introduction 411
16.2 Basic Resampling Concepts 414
16.3 Time Series Resampling 415
16.3.1 Residue Resampling 417
16.3.2 Phase Resampling 418
16.3.3 Other Resampling Methods 420
16.4 Numerical Examples and Applications 420
16.4.1 Simulated Data 420
16.4.2 Real Data 426
16.5 Discussion 431
16.6 Conclusions 433
References 433
17 Granger Causality: Basic Theory and Application to Neuroscience
(Mingzhou Ding, Yonghong Chen, and Steven L. Bressler) 437
17.1 Introduction 437
17.2 Bivariate Time Series and Pairwise Granger Causality 438
17.2.1 Time Domain Formulation 438
17.2.2 Frequency Domain Formulation 440
17.3 Trivariate Time Series and Conditional Granger Causality 443
17.3.1 Time Domain Formulation 444
xii Contents
17.3.2 Frequency Domain Formulation 445
17.4 Estimation of Autoregressive Models 447
17.5 Numerical Examples 449
17.5.1 Example 1 449
17.5.2 Example 2 451
17.5.3 Example 3 452
17.6 Analysis of a Beta Oscillation Network in Sensorimotor Cortex . . 454
17.7 Summary 459
References 459
18 Granger Causality on Spatial Manifolds:
Applications to Neuroimaging
(Pedro A. ValMs Sosa, Jose Miguel Bornot Sdnchez, Mayrim Vega Hernandez, 461
Lester Melie Garcia, Agustin Lage Castellanos, and Erick Canales Rodriguez)
18.1 Introduction 462
18.2 The Continuous Spatial Multivariate Autoregressive Model
and its Discretization 464
18.3 Testing for Spatial Granger Causality 466
18.4 Dimension Reduction Approaches to sMAR Models 468
18.4.1 ROI Based Causality Analysis 468
18.4.2 Latent Variable Based Causality Analysis 469
18.5 Penalized sMAR 471
18.5.1 General Model 471
18.5.2 Achieving Sparsity Via Variable Selection 474
18.5.3 Achieving Spatial Smoothness 476
18.5.4 Achieving Sparseness and Smoothness 477
18.6 Estimation via the MM Algorithm 478
18.7 Evaluation of Simulated Data 481
18.8 Influence Fields for Real Data 482
18.9 Possible Extensions and Conclusions 485
References 485
Index 493 |
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| indexdate | 2024-07-09T20:43:08Z |
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