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下载 Applied Nonlinear Time Series Analysis - Applications in Physics, Physiology and Finance
2005
261pages

Contents
Preface vii
1. Time series embedding and reconstruction 1
1.1 Stochasticity and determinism: Why should we bother? . . 2
1.2 Embedding dimension 5
1.2.1 False Nearest Neighbours 6
1.2.2 False strands and so on 7
1.2.3 Embed, embed and then embed 8
1.2.4 Embed and model, and then embed again 9
1.3 Embedding lag 10
1.3.1 Autocorrelation 10
1.3.2 Mutual information 11
1.3.3 Approximate period 11
1.3.4 Generalised embedding lags 12
1.4 Which comes first? 14
1.5 An embedding zoo 15
1.6 Irregular embeddings 19
1.6.1 Finding irregular embeddings 21
1.7 Embedding window 28
1.7.1 A modelling paradigm 30
1.7.2 Examples 34
1.8 Application: Sunspots and chaotic laser dynamics:
Improved modelling and superior dynamics 41
1.9 Summary 44


2. Dynamic measures and topological invariants 47

2.1 Correlation dimension 48
2.2 Entropy, complexity and information 54
2.2.1 Entropy 54
2.2.2 Complexity 58
2.2.3 Alternative encoding schemes 60
2.3 A p p l i c a t i o n : D e t e c t i n g v e n t r i c u l a r a r r h y t h m i a . . . . 69
2.4 Lyapunov exponents and nonlinear prediction error 74
2.5 Application: Potential predictability in financial
time series 80
2.6 Summary 82


3. Estimation of correlation dimension 85
3.1 Preamble 86
3.2 Box-counting and the Grassberger-Procaccia algorithm . . . 87
3.3 Judd's algorithm 90
3.4 Application: Distinguishing sleep states by monitoring
respiration 95
3.5 The Gaussian Kernel algorithm 102
3.6 Application: Categorising cardiac dynamics from
measured ECG 105
3.7 Even more algorithms Ill


4. The method of surrogate data 115
4.1 The rationale and language of surrogate data 116
4.2 Linear surrogates 120
4.2.1 Algorithm 0 and its analogues 121
4.2.2 Algorithm 1 and its applications 122
4.2.3 Algorithm 2 and its problems 123
4.3 Cycle shuffled surrogates 125
4.4 Test statistics 129
4.4.1 The Kolmogorov-Smirnov test 131
4.4.2 The X
2 test 131
4.4.3 Noise dimension 132
4.4.4 Moments of the data 132
4.5 Correlation dimension: A pivotal test statistic — linear hypotheses
133
4.5.1 The linear hypotheses 135
4.5.2 Calculations 136
4.5.3 Results 142
Contents xiii
4.6 Application: Are financial time series deterministic? 143
4.7 Summary 147


5. Non-standard and non-linear surrogates 149
5.1 Generalised nonlinear null hypotheses: The hypothesis is the
model 150
5.1.1 The "pivotalness" of dynamic measures 152
5.1.2 Correlation dimension: A pivotal test statistic — nonlinear
hypothesis 153
5.2 Application: Infant sleep apnea 155
5.3 Pseudo-periodic surrogates 157
5.3.1 Shadowing surrogates 158
5.3.2 The parameters of the algorithm 161
5.3.3 Linear noise and chaos 163
5.4 Application: Mimicking human vocalisation patterns 166
5.5 Application: Are financial time series really deterministic?
168
5.6 Simulated annealing and other computational methods . . . 174
5.7 Summary 176


6. Identifying the dynamics 179
6.1 Phenomenological and ontological models 180
6.2 Application: Severe Acute Respiratory Syndrome:
Assessing governmental control strategies during the
SARS outbreak in Hong Kong 181
6.3 Local models 195
6.4 The importance of embedding for modelling 198
6.5 Semi-local models 200
6.5.1 Radial basis functions 200
6.5.2 Minimum description length principle 201
6.5.3 Pseudo linear models 205
6.5.4 Cylindrical basis models 207
6.6 Application: Predicting onset of Ventricular Fibrillation,
and evaluating time since onset 208
7. Applications 223
Bibliography 229
Index 241

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