  Multi-electrode neurophysiological recordings produce massive quantities of
data. Multivariate time series analysis provides the basic framework for
analyzing the patterns of neural interactions in these data. It has long been
recognized that neural interactions are directional. Being able to assess the
directionality of neuronal interactions is thus a highly desired capability for
understanding the cooperative nature of neural computation. Research over the
last few years has shown that Granger causality is a key technique to furnish
this capability. The main goal of this article is to provide an expository
introduction to the concept of Granger causality. Mathematical frameworks for
both bivariate Granger causality and conditional Granger causality are
developed in detail with particular emphasis on their spectral representations.
The technique is demonstrated in numerical examples where the exact answers of
causal influences are known. It is then applied to analyze multichannel local
field potentials recorded from monkeys performing a visuomotor task. Our
results are shown to be physiologically interpretable and yield new insights
into the dynamical organization of large-scale oscillatory cortical networks.
