Overview

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 random­ ness. For statisticians working within the traditional statistical framework, the task of critically assimilating randomness generated by a purely de­ 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 con­ 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 Stud­ ies, University of British Columbia and the graduate courses on Time Series Analysis at the University of Iowa, the University of Hong Kong, the Lon­ 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 Shi­ mada, Floris Takens and Qiwei Yao.

Full Product Details

Author:   Kung-Sik Chan ,  Howell Tong
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 1st ed. 2001
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.498kg
ISBN:  

9781441929365

ISBN 10:   1441929363
Pages:   300
Publication Date:   23 November 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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 §3.3.2.- B.3 Shadowing and Hyperbolic Attractors.- Appendix C Data Sets and Software.- References.- Author Index.

Reviews

From the reviews: SHORT BOOK REVIEWS The authors have done an excellent job, providing an overview of known results with detailed references to the literature, as well as pointing out some open problems. In general, the book serves to `encourage more statisticians to join in with the fun of chaos'. The book fills a gap in the need to overview the present state of statistics and to point into the right direction for research. It seems to me that this has been achieved by the authors in an excellent way. Chan and Tong's book certainly deserves recommendation to anyone who is interested in dynamics, either as a statistician or as a researcher in the theory of dynamical systems, ergodic theory or differential equations. (Manfred Denker, Metrika, September, 2003) The authors fully attain their aim stated in the introduction. Their style is very friendly and they take much care to prevent technical details from obscuring the essential issues. The book requires careful reading but the profit is well worth the effort. A truly enjoyable and recommendable book! (Ricardo Maronna, Statistical Papers, Vol. 44 (1), 2003)

From the reviews: SHORT BOOK REVIEWS The authors have done an excellent job, providing an overview of known results with detailed references to the literature, as well as pointing out some open problems. In general, the book serves to 'encourage more statisticians to join in with the fun of chaos'. The book fills a gap in the need to overview the present state of statistics and to point into the right direction for research. It seems to me that this has been achieved by the authors in an excellent way. Chan and Tong's book certainly deserves recommendation to anyone who is interested in dynamics, either as a statistician or as a researcher in the theory of dynamical systems, ergodic theory or differential equations. (Manfred Denker, Metrika, September, 2003) The authors fully attain their aim stated in the introduction. Their style is very friendly and they take much care to prevent technical details from obscuring the essential issues. The book requires careful reading but the profit is well worth the effort. A truly enjoyable and recommendable book! (Ricardo Maronna, Statistical Papers, Vol. 44 (1), 2003)

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