Interdisciplinary application of nonlinear time series methods

Abstract

This paper reports on the application to field measurements of time series\nmethods developed on the basis of the theory of deterministic chaos. The major\ndifficulties are pointed out that arise when the data cannot be assumed to be\npurely deterministic and the potential that remains in this situation is\ndiscussed. For signals with weakly nonlinear structure, the presence of\nnonlinearity in a general sense has to be inferred statistically. The paper\nreviews the relevant methods and discusses the implications for deterministic\nmodeling. Most field measurements yield nonstationary time series, which poses\na severe problem for their analysis. Recent progress in the detection and\nunderstanding of nonstationarity is reported. If a clear signature of\napproximate determinism is found, the notions of phase space, attractors,\ninvariant manifolds etc. provide a convenient framework for time series\nanalysis. Although the results have to be interpreted with great care, superior\nperformance can be achieved for typical signal processing tasks. In particular,\nprediction and filtering of signals are discussed, as well as the\nclassification of system states by means of time series recordings.\n