Nonlinear time series analysis. 2nd, extended ed. (English) Zbl 1050.62093

Kantz, Holger; Schreiber, Thomas

Cambridge University Press (ISBN 0-521-52902-6/pbk; 0-521-82150-9/hbk). xvi, 369 p. (2004).

The book provides experimental researchers in nonlinear dynamical systems (biology, physiology, geophysics, economics and others) with methods for processing and analysing measured signals. It is oriented to practical appliations without mathematical proofs. In difference from the conventional nonlinear time series monographs (ARCH, threshold models, etc.) it is devoted more to the analysis of nonlinear dynamical systems, including chaotic data from the experimental point of view. This second edition not only extends the first one from 1997, see the review Zbl 0873.62085, by new chapters, but it makes use of routines of the software package TISEAN written by R. Hegger and the authors of the book (TISEAN is publicly available from http://www.mpipks-dresden.mpg.de/~tisean).
The particular chapters are the following: Ch. 2: Linear tools and general considerations; Ch. 3: Phase space methods; Ch. 4: Determinism and predictability; Ch. 5: Instability; Ch. 6: Self-similarity; Ch. 7: Using nonlinear methods when determinism is weak; Ch. 8: Selected nonlinear phenomena (e.g., limit cycles, bifurcations, and others); Ch. 9: Advanced embedding methods; Ch. 10: Chaotic data and noise; Ch. 11: More about invariant quantities; Ch. 12: Modelling and forecasting; Ch. 13: Nonstationary signals; Ch. 14: Coupling and synchronisation of nonlinear systems; Ch. 15: Chaos control.

Reviewer: Tomáš Cipra (Praha)

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
37M10	Time series analysis of dynamical systems
62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62-02	Research exposition (monographs, survey articles) pertaining to statistics
62-04	Software, source code, etc. for problems pertaining to statistics

Keywords:

chaos; random noise; nonlinear time series analysis; TISEAN

Software:

TISEAN