Inferring Indirect Coupling by Means of Recurrences

The identification of the coupling direction from measured time series taking place in a group of interacting components is an important challenge for many experimental studies. We propose here a method to uncover the coupling configuration using recurrence properties. The approach hinges on a generalization of conditional probability of recurrence, which was originally introduced to detect and quantify even weak coupling directions between two interacting systems, to the case of multivariate time series where indirect interactions might be present. We test our method by an example of three coupled Lorenz systems. Our results confirm that the proposed method has much potential to identify indirect coupling, which is very relevant for experimental time series analysis.