Robust methods to detect coupling among nonlinear dynamic time series

Abstract

Two numerical methods are proposed for detection of coupling between multiple time series generated by deterministic nonlinear systems. The first detects interdependence or the existence of coupling between time series. The second ascertains directionality of coupling, or alternatively, latent coupling, the case when multiple series are driven by another, unobserved system. In either case, the driver and the recipients of the coupling may be periodic or aperiodic, and in particular may be chaotic. The only inputs to the method are two or more simultaneously recorded time series. The methods rely solely on ranking distances between states in time-delay reconstructions of the data, and for that reason tend to be robust to observational noise.