NONLINEAR TIME SERIES ANALYSIS
This book represents a modern approach to time series analysis which is based on
the theory of dynamical systems. It starts from a sound outline of the underlying
theory to arrive at very practical issues, which are illustrated using a large number of
empirical data sets taken from various fields. This book will hence be highly useful
for scientists and engineers from all disciplines who study time variable signals,
including the earth, life and social sciences.
The paradigm of deterministic chaos has influenced thinking in many fields of
science. Chaotic systems show rich and surprising mathematical structures. In the
applied sciences, deterministic chaos provides a striking explanation for irregular
temporal behaviour and anomalies in systems which do not seem to be inherently
stochastic. The most direct link between chaos theory and the real world is the anal-
ysis of time series from real systems in terms of nonlinear dynamics. Experimental
technique and data analysis have seen such dramatic progress that, by now, most
fundamental properties of nonlinear dynamical systems have been observed in the
laboratory. Great efforts are being made to exploit ideas from chaos theory where-
ver the data display more structure than can be captured by traditional methods.
Problems of this kind are typical in biology and physiology but also in geophysics,
economics and many other sciences.
This revised edition has been significantly rewritten an expanded, including
several new chapters. In view of applications, the most relevant novelties will be the
treatment of non-stationary data sets and of nonlinear stochastic processes inside
the framework of a state space reconstruction by the method of delays. Hence, non-
linear time series analysis has left the rather narrow niche of strictly deterministic
systems. Moreover, the analysis of multivariate data sets has gained more atten-
tion. For a direct application of the methods of this book to the reader’s own data
sets, this book closely refers to the publicly available software package TISEAN.
The availability of this software will facilitate the solution of the exercises, so that
readers now can easily gain their own experience with the analysis of data sets.
Holger Kantz, born in November 1960, received his diploma in physics from
the University of Wuppertal in January 1986 with a thesis on transient chaos. In
January 1989 he obtained his Ph.D. in theoretical physics from the same place,
having worked under the supervision of Peter Grassberger on Hamiltonian many-
particle dynamics. During his postdoctoral time, he spent one year on a Marie Curie
fellowship of the European Union at the physics department of the University of
