Nonlinear Dynamics and Time Series

Nonlinear Dynamics and Time Series : Building a Bridge Between the Natural and Statistical Sciences

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Description

This book is a collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics (in the physiological and biological sciences) and statistics. It presents the proceedings of a four-day workshop entitled ""Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences"" held at the Centre de Recherches Mathematiques (CRM) in Montreal in July 1995. The goal of the workshop was to provide an exchange forum and to create a link between two diverse groups with a common interest in the analysis of nonlinear time series data. The editors and peer reviewers of this work have attempted to minimize the problems of maintaining communication between the different scientific fields. The result is a collection of interrelated papers that highlight current areas of research in statistics that might have particular applicability to nonlinear dynamics and new methodology and open data analysis problems in nonlinear dynamics that might find their way into the toolkits and research interests of statisticians.Features: A survey of state-of-the-art developments in nonlinear dynamics time series analysis with open statistical problems and areas for further research. Contributions by statisticians to understanding and improving modern techniques commonly associated with nonlinear time series analysis, such as surrogate data methods and estimation of local Lyapunov exponents. Starting point for both scientists and statisticians who want to explore the field. Expositions that are readable to scientists outside the featured fields of specialization. Information for our distributors: Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
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Product details

  • Paperback | 252 pages
  • Providence, United States
  • English
  • 0821841858
  • 9780821841853

Table of contents

Opening lectures: Tools for the analysis of chaotic data by H. I. Abarbanel Some comments on nonlinear time series analysis by H. Tong Embeddings, dimension, and system reconstruction: A general approach to predictive and fractal scaling dimensions in discrete-index time series by C. D. Cutler Statistics for continuity and differentiability: An application to attractor reconstruction from time series by L. M. Pecora, T. L. Carroll, and J. F. Heagy Reconstruction of integrate-and-fire dynamics by T. Sauer Surrogate data methodology: On the validity of the method of surrogate data by K.-S. Chan Using "surrogate surrogate data" to calibrate the actual rate of false positives in tests for nonlinearity in time series by J. Theiler and D. Prichard Local Lyapunov exponents: Chaos with confidence: Asymptotics and applications of local Lyapunov exponents by B. A. Bailey, S. Ellner, and D. W. Nychka Estimating local Lyapunov exponents by Z.-Q. Lu and R. L. Smith Long-range dependence: Defining and measuring long-range dependence by P. Hall Modelling nonlinearity and long memory in time series by P. M. Robinson and P. Zaffaroni Data analysis and applications: Ergodic distributions of random dynamical systems by L. M. Berliner, S. N. MacEachern, and C. S. Forbes Detecting structure in noise by L. Borland Characterizing nonlinearity in weather and epilepsy data: A personal view by M. C. Casdagli Assessment of linear and nonlinear correlations between neural firing events by A. Longtin and D. M. Racicot Markov chain methods in the analysis of heart rate variability by S. J. Merrill and J. R. Cochran.
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