Methods of nonlinear time series analysis are discussed from a dynamical systems perspective on the one hand, and from a statistical perspective on the other. After giving an informal overview of the theory of dynamical systems relevant to the analysis of deterministic time series, time series generated by nonlinear stochastic systems and spatio-temporal dynamical systems are considered. Several statistical methods for the analysis of nonlinear time series are presented and illustrated with applications to physical and physiological time series.
Nonlinear Time Series Analysis: Methods And Applications
Nonlinear dynamical systems; stochastic time series; a test for reversability; detecting differences between reconstruction measures; estimating invariants of noisy attractors; the correlation integral of noisy attractors; spiral wave tip dynamics; spatio-temporal chaos - a solvable model.