Surrogate-based test for Granger causality

An approach for testing the presence of Granger causality between two time series is proposed. The residue of the destination signal after self-prediction is computed, after which a cross-prediction of the source signal over this residue is examined. In the absence of causality, there should be no cross-predictive power, due to which the performance of the cross-prediction system can be used as an indication of causality. The proposed approach uses the surrogate data method, and implements the self- and cross-prediction systems as feedforward neural networks. It is tested on synthetic examples, and a sensitivity analysis demonstrates the robustness of the approach.