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Surrogate-based hypothesis test without surrogates

  • Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1

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Author:M. Thiel, Maria Carmen Romano, Udo Schwarz, Jürgen KurthsORCiDGND, Jens Timmer
Document Type:Article
Year of first Publication:2004
Year of Completion:2004
Release Date:2017/03/24
Source:International Journal of Bifurcation and Chaos. - ISSN 0218-1274. - 14 (2004), 6, S. 2107 - 2114
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik