Linear versus nonlinear time series analysis-smoothed correlation integrals

The classical analysis of stationary time series is based on the study of autocovariances and spectra. This type of analysis is especially suitable for Gaussian time series. After it became known that also nonlinear deterministic systems can behave in a seemingly random (chaotic) way, methods were developed to detect such nonlinear (and deterministic) sources. These methods are to a large extend based on the use of correlation integrals. Though it is known that these two methods of analysis provide information which is in some sense complementary, not much is known about the possible relations between the information they provide. In this paper we investigate the correlation integrals, and the quantities which can be derived from them, of Gaussian time series in terms of their autocovariances and spectra. (C) 2003 Elsevier B.V. All rights reserved.