Nonlinear Time Series Analysis (Cambridge Nonlinear Science Series, Series Number 7)

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.

Deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which seem not to be inherently stochastic. This book describes the most direct link between chaos theory and the real world, which is the analysis of time series from real systems in terms of nonlinear dynamics.