Bivariate surrogate techniques: Necessity, strengths, and caveats

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 testagainst a different null hypothesis, e.g., an underlying bivariate linear stochastic process. Two measures thataim at a characterization of interdependence between nonlinear deterministic dynamics were used as discriminatingstatistics. We analyze eight different stochastic and deterministic models not only to demonstrate thepower of the surrogates, but also to reveal some pitfalls and limitations.