Detection of Nonlinearity and Chaos in Time Series

Abstract

A method for identification of nonlinearity and chaos in time series is presented. Nonlinearity is tested using a procedure which combines redundancy and surrogate data techniques. After positive identification of the nonlinear character of the data under study, the possible presence of underlying chaotic dynamics can be assessed by a marginal redundancy approach, because of the direct relationship of the marginal redundancy to the Kolmogorov-Sinai entropy of the dynamical system that generates the data. 1 Introduction Ideas and concepts from nonlinear dynamics and deterministic chaos theory have led to a number of algorithms which are able, in principle, to identify and quantify underlying nonlinear deterministic/chaotic dynamics in time series (Abraham et al. 1989, Grassberger & Procaccia 1983, Mayer-Kress 1986). After extensive use, however, many of these algorithms were found to be chronically unreliable, often This article (further referred to as article [I]) was written as a ..