Investigation of nonlinear granger causality in the context of epilepsy

Granger causality approaches have been widely used to estimate effective connectivity in complex dynamic systems. These techniques are based on the building of predictive models which not only depend on a proper selection of the predictive vectors size but also on the chosen class of regression functions. The question addressed in this paper is the estimation of the model order in the computation of Granger causality indices to characterize the propagation flow between simulated epileptic signals. In this contribution, a new strategy is proposed to select a suitable model order for potentially nonlinear systems. A nonlinear vectorial autoregressive model based on a wavelet network is considered for the identification and an optimal nonlinear model order is selected using the Bayesian information criterion and imported in nonlinear kernel predictors to derive Granger causality. Simulations are firstly conducted on a linear autoregressive model, then on toy nonlinear models and, finally, on simulated intracranial electroencephalographic signals obtained from an electrophysiology based model to reveal the directional relationships between time series data. The performance of our approach proves the effectiveness of the new strategy in the Granger index estimation.