On the performance of temporal Granger causality measurements on time series: a comparative study

Abstract

Nowadays, Granger causality techniques are frequently applied to investigate complex dynamical systems such as brain networks. Indeed, various derivations have been proposed from the initially basic definition of the Granger causality concept to deal with two fundamental issues of how to cope with dynamical nonlinearities when they are present and how to prevent model over fitting, i.e., how to eliminate nonsignificant regressors. In this paper, a comparative study is conducted on four methods facing differently these issues, namely the multivariate linear Granger causality, the kernel Granger causality, the restricted Granger causality and the nonlinear Granger causality, the latter relying on the nonlinear Wavelet Network vectorial autoregressive model. For an objective comparison of these methods, a new strategy is proposed to derive linear and nonlinear partial model orders to be applied, respectively, to the multivariate linear Granger causality and the nonlinear Granger causality methods which generally use a global model order.