A Parametric Method to Measure Time-Varying Linear and Nonlinear Causality With Applications to EEG Data

Abstract

A linear and nonlinear causality detection method called the error-reduction-ratio causality (ERRC) test is introduced in this paper to investigate if linear or nonlinear models should be considered in the study of human electroencephalograph (EEG) data. In comparison to the traditional Granger methods, one significant advantage of the ERRC approach is that it can effectively detect the time-varying linear and nonlinear causalities between two signals without fitting a complete nonlinear model. Two numerical simulation examples are employed to compare the performance of the new method with other widely used methods in the presence of noise and in tracking time-varying causality. Finally, an application to measure the linear and nonlinear relationships between two EEG signals from different cortical sites for patients with childhood absence epilepsy is discussed.