Summary: Bivariate surrogate techniques: Necessity, strengths, and caveats
Ralph G. Andrzejak,1,
* Alexander Kraskov,1
and Thomas Kreuz1,2
John-von-Neumann Institute for Computing, Forschungszentrum Jušlich, 52425 Jušlich, Germany
Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany
Received 28 May 2003; published 15 December 2003
The concept of surrogates allows testing results from time series analysis against specified null hypotheses.
In application to bivariate model dynamics we here compare different types of surrogates, each designed to test
against a different null hypothesis, e.g., an underlying bivariate linear stochastic process. Two measures that
aim at a characterization of interdependence between nonlinear deterministic dynamics were used as discrimi-
nating statistics. We analyze eight different stochastic and deterministic models not only to demonstrate the
power of the surrogates, but also to reveal some pitfalls and limitations.
DOI: 10.1103/PhysRevE.68.066202 PACS number s : 05.45.Tp, 05.45.Xt, 05.10.Ln, 05.40.Ca
Univariate nonlinear time series analysis provides a num-