Surrogate-based hypothesis test without surrogates

Marco Thiel, M Carmen Romano, U. Schwarz, Juergen Kurths, J. Timmer

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)2107-2114
Number of pages8
JournalInternational Journal of Bifurcation and Chaos
Issue number6
Publication statusPublished - Jun 2004


  • Fourier surrogates
  • nonlinear time series analysis
  • time-series
  • cygnus X-1
  • nonlinearity
  • variability


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