Nonlinear Time Series Analysis

by Holger Kantz, Thomas Schreiber

Deterministic chaos provides a novel framework for the analysis of irregular time series. Traditionally, nonperiodic signals are modeled by linear stochastic processes. But even very simple chaotic dynamical systems can exhibit strongly irregular time evolution without random inputs. Chaos theory offers completely new concepts and algorithms for time series analysis which can lead to a thorough understanding of the signal. The book introduces a broad choice of such concepts and methods, including phase space embeddings, nonlinear prediction and noise reduction, Lyapunov exponents, dimensions and entropies, as well as statistical tests for nonlinearity. Related topics like chaos control, wavelet analysis and pattern dynamics are also discussed. Applications range from high quality, strictly deterministic laboratory data to short, noisy sequences which typically occur in medicine, biology, geophysics or the social sciences. All material is discussed and illustrated using real experimental data.

Genres: Science, Mathematics, Textbooks, Economics, Physics

320 pages, Paperback

First published September 28, 1997

Reviews

[Robert]

This book makes an excellent attempt to clearly explain a topic that is conceptually difficult, mathematically obscure (and potentially difficult...) and fraught with pitfalls that have trapped many, many unwary but enthusiastic scientists. The early chapters build on each other logically and provide a usable entry into the field and its practicalities. The later "advanced topics" represent a significant jump in difficulty, requiring a wide range of mathematical techniques that are assumed rather than explained, and are really only a good jumping off point into the wider literature on some really esoteric subjects...

[Riccardo]

Essential reading, providing an impressive overview of the field. But the explanations often skip on details and conceptual explanations. Hard read.