Author | Chan, Kung-Sik. author |
---|---|

Title | Chaos: A Statistical Perspective [electronic resource] / by Kung-Sik Chan, Howell Tong |

Imprint | New York, NY : Springer New York : Imprint: Springer, 2001 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-3464-5 |

Descript | XVI, 300 p. online resource |

SUMMARY

It was none other than Henri Poincare who at the turn of the last century, recognised that initial-value sensitivity is a fundamental source of randomยญ ness. For statisticians working within the traditional statistical framework, the task of critically assimilating randomness generated by a purely deยญ terministic system, often known as chaos, is an intellectual challenge. Like some other statisticians, we have taken up this challenge and our curiosity as reporters and participants has led us to investigate beyond the earlier discoveries in the field. Earlier statistical work in the area was mostly conยญ cerned with the estimation of what is sometimes imprecisely called the fractal dimension. During the different stages of our writing, substantial portions of the book were used in lectures and seminars. These include the DMV (German Mathematical Society) Seminar Program, the inaugural session of lectures to the Crisis Points Project at the Peter Wall Institute of Advanced Studยญ ies, University of British Columbia and the graduate courses on Time Series Analysis at the University of Iowa, the University of Hong Kong, the Lonยญ don School of Economics and Political Science, and the Chinese University of Hong Kong. We have therefore benefitted greatly from the comments and suggestions of these audiences as well as from colleagues and friends. We are grateful to them for their contributions. Our special thanks go to Colleen Cutler, Cees Diks, Barbel FinkensHidt, Cindy Greenwood, Masakazu Shiยญ mada, Floris Takens and Qiwei Yao

CONTENT

1 Introduction and Case Studies -- 2 Deterministic Chaos -- 3 Chaos and Stochastic Systems -- 4 Statistical Analysis I -- 5 Statistical Analysis II -- 6 Nonlinear Least-Square Prediction -- 7 Miscellaneous Topics -- Appendix A Deterministic Chaos -- A.1 Introduction -- A.2 Attracting Sets -- A.3 Another Look At the Logistic Maps -- A.4 Attractors -- A.5 Two Approaches to Studying Chaos -- A.6 Invariant and Ergodic Distributions -- A.7 Lyapunov Exponents -- A.8 Natural Measures -- A.9 Dimensions of an Attractor -- A.9.1 Box-Counting Dimension -- A.9.2 Correlation Dimension -- A.10 Map Reconstruction -- A. 11 Some Elements of Differentiable Manifolds -- A.12 Hyperbolic Sets -- A.13 Notes -- Appendix B Supplements to Chapter 3 -- B.1 Criteria for Ergodicity -- B.1.1 Notes -- B.2 Proofs of Two Theorems in ยง3.3.2 -- B.3 Shadowing and Hyperbolic Attractors -- Appendix C Data Sets and Software -- References -- Author Index

Statistics
Chemometrics
Probabilities
Statistical physics
Dynamical systems
Computational intelligence
Statistics
Statistical Theory and Methods
Computational Intelligence
Math. Applications in Chemistry
Statistical Physics Dynamical Systems and Complexity
Probability Theory and Stochastic Processes