Multivariate analysis of dynamical processes with applications to the neurosciences

Nowadays, data are recorded with increasing spatial and temporal resolution. Commonly these data are analyzed using univariate or bivariate approaches. Most of the analysis techniques assume stationarity of the underlying dynamical processes. Here, we present an approach that is capable of analyzing multivariate data, the so-called renormalized partial directed coherence. It utilizes the concept of Granger causality and is applicable to non-stationary data. We discuss its abilities and limitations, and demonstrate its usefulness in an application to murine electroencephalography (EEG) data during sleep transitions.