  We consider extension of Granger causality to nonlinear bivariate time
series. In this frame, if the prediction error of the first time series is
reduced by including measurements from the second time series, then the second
time series is said to have a causal influence on the first one. Not all the
nonlinear prediction schemes are suitable to evaluate causality, indeed not all
of them allow to quantify how much the knowledge of the other time series
counts to improve prediction error. We present a novel approach with bivariate
time series modelled by a generalization of radial basis functions and show its
application to a pair of unidirectionally coupled chaotic maps and to a
physiological example.
