Robust methods to detect coupling among nonlinear dynamic time series

Two numerical methods are proposed to detect and analyze coupling in time series from deterministic nonlinear systems. The first identifies the presence of coupling or interdependence, while the second determines the directionality of coupling. The second method can also identify latent coupling-series that are not directly coupled but are correlated due to influence by another, unobserved system. Both methods accommodate periodic, aperiodic, and chaotic dynamics, and use order statistics derived from relative distances within a time-delay embedding. The methods are intended to be practical and apply to data sets consisting of simultaneous system recordings, and robust to observational noise due to their use of order statistics.