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Abstract: The linear Granger approach, to detect cause-effect relationships between two time series, is generalized to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and two physiological data-set are presented.