Detecting functional relationships between simultaneous time series

We describe a method to characterize the predictability and functionality between two simultaneously generated time series. This nonlinear method requires minimal assumptions and can be applied to data measured either from coupled systems or from different positions on a spatially extended system. This analysis generates a function statistic, Theta(c(0)), that quantifies the level of predictability between two time series. We illustrate the utility of this procedure by presenting results from a computer simulation and two experimental systems.