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Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences
Edited by: Colleen D. Cutler, University of Waterloo, ON, Canada, and Daniel T. Kaplan, McGill University, Montreal, QC, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
1997; 252 pp; softcover
Volume: 11
ISBN-10: 0-8218-4185-8
ISBN-13: 978-0-8218-4185-3
List Price: US$91
Individual Members: US$54.60
Institutional Members: US$72.80
Order Code: FIC/11.S
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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 Mathématiques (CRM) in Montréal 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.


  • 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.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Graduate students, mathematicians, statisticians, nonlinear dynamicists, physicists, and biologists from all fields who are interested in using nonlinear dynamics techniques to study their time series data.


"An important inter-disciplinary work ... provides a valuable collection of recent research ... should appeal to scientists and statisticians who are relatively new to the field and to others interested in a very readable exploration of the topics covered."

-- Journal of Computational Intelligence in Finance

Table of Contents

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