Nonlinear time series analysis

H. Kantz and T. Schreiber
Nonlinear time series analysis

'Nonlinear Time Series Analysis' by H Kantz and T Schreiber is published by Cambridge University Press in the Cambridge Nonlinear Science series. Price £ 50 (UK) or $ 74.95 (USA) (hardback), ISBN 0521 551447. Ordering information from Cambridge University Press.

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. Also related topics like chaos control, wavelet analysis and pattern dynamics are 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. For the main algorithms, sample computer programs in C and FORTRAN are given. For the convenience of our readers, the sample programs can also be downloaded from this server.

Part one: Basic topics

Part two: Advanced topics