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 analysis 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 wherever 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, nonlinear time series analysis has left the rather narrow niche of strictly deterministic systems. Moreover, the analysis of multivariate data sets has gained more attention. 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.