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Nonlinear time series analysis. (English) Zbl 0873.62085
Cambridge Nonlinear Science Series. 7. Cambridge: Cambridge University Press. xvi, 304 p. (1997).
This book deals with analysis of experimental time series data in cases where linear methods of time series analysis fail. Irregular behaviour of time series may be modeled by nonlinear dynamic systems perturbed by random noise. The analysis of such systems leads to chaos theory. The methods of chaos theory are demonstrated in examples from natural science, technique and medicine. This includes such methods and definitions as: Phase space embedding, nonlinear prediction, noise reduction, Lyapunov exponent, dimension, entropy, time delay, attractor, transience, stability, ergodicity, bifurcation, intermittency, chaos control, wavelet analysis. References to further literature and some exercises are included at the end of the 11 chapters. FORTRAN programs for some of the algorithms are given in the appendix.
The book doesn’t contain exact definitions and theorems with proofs, but it verbally speaks about concepts, ideas and methods of nonlinear time series analysis using formulas and figures. It is recommended for graduate students and researchers who have the problem to find the content of information in experimental process data from physics, geophysics, chemistry, biology, medicine etc. It is also useful for theorists to see some applications and practical methods.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93E10 Estimation and detection in stochastic control theory
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62-04 Software, source code, etc. for problems pertaining to statistics
60G35 Signal detection and filtering (aspects of stochastic processes)