A new NARX-based Granger linear and nonlinear casual influence detection method with applications to EEG data

A new NARX-based Granger linear and nonlinear casual influence detection method is presented in this paper to address the potential for linear and nonlinear models in data with applications to human EEG data analysis. Considering two signals initially, the paper introduces four indexes to measure the linearity and nonlinearity of a single signal, and one signal influencing the second signal. This method is then extended to the time-varying and multivariate cases. An adaptation of an Orthogonal Least Squares routine is employed to select the significant terms in the models. A numerical example is provided to illustrate the effectiveness of the new algorithms together with the application to real EEG data collected from 4 patients.

► A new linear and nonlinear causality detection algorithm is derived.
► Four indices are introduced to measure the linearity and nonlinearity of signals.
► These methods are then extended to the time varying case.
► Real applications to EEG data are described.