## Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and FinanceNonlinear time series methods have developed rapidly over a quarter of a century and have reached an advanced state of maturity during the last decade. Implementations of these methods for experimental data are now widely accepted and fairly routine; however, genuinely useful applications remain rare. This book focuses on the practice of applying these methods to solve real problems. To illustrate the usefulness of these methods, a wide variety of physical and physiological systems are considered. The technical tools utilized in this book fall into three distinct, but interconnected areas: quantitative measures of nonlinear dynamics, MonteOCoCarlo statistical hypothesis testing, and nonlinear modeling. Ten highly detailed applications serve as case studies of fruitful applications and illustrate the mathematical techniques described in the text." |

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### Contents

Preface | 1 |

Dynamic measures and topological invariants | 47 |

Estimation of correlation dimension | 85 |

The method of surrogate data | 115 |

Nonstandard and nonlinear surrogates | 149 |

ministic? | 168 |

Identifying the dynamics | 179 |

Applications | 223 |

229 | |

241 | |

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### Common terms and phrases

application approximately arrhythmia attractor autocorrelation behaviour bifurcation parameter calculations cardiac arrhythmia chaos chaotic chapter complexity computed consistent correlation dimension estimates correlation integral cycle shuffled data and surrogates data set dc(eo delay embedding described dimensional dynamic invariants dynamical system embedding dimension embedding lag embedding strategy entropy estimation of correlation false nearest neighbours Gaussian noise Ikeda Ikeda map infection length scales linearly filtered noise Lyapunov exponents measure Menger Sponge method minimum description length model prediction error modelling algorithm mutual information noise level nonlinear models nonlinear prediction error nonlinear time series NP CD+NP null hypothesis observed onset optimal model panel periodic orbit pivotal plot PPS algorithm probability density probability distribution problem pseudo-periodic random realisations reconstruction recordings reject Rossler system sampling selection series data signal simulations sinus rhythm standard deviation surrogate data techniques test statistic trajectory typical underlying dynamics values ventricular ventricular fibrillation