Methods for Quantifying the Causal Structure of Bivariate Time Series

In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear methods ineffective. Moreover, signals sampled from real world systems are noisy and short, posing additional constraints on the estimation of the underlying couplings. In this article, we compare a set of six recently introduced methods for quantifying the causal structure of bivariate time series extracted from systems with complex dynamical behavior. We discuss the usefulness of the methods for detecting asymmetric couplings and directional flow of information in the context of uni- and bidirectionally coupled deterministic chaotic systems.