《Handbook of Time Series Analysis-ch17 Granger Causality》.pdf

Handbook of Time Series Analysis Recent Theoretical Developments and Applications ion Theory Edited by Bjorn Schelter, MatthiasWinterhalder, and Jens Timmer WILEY- VCH WILEY-VCH Verlag GmbH Co. KGaA 17 Granger Causality: Basic Theory and Application to Neuroscience Mingzhou Ding, Yonghong Chen,and Steven L. Bressler Multielectrode neurophysiological recordings produce massive quantities of da- ta. 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 chapter is to provide an expository introduction to the concept of Granger causality. Mathematical frameworks for both the bivariate Granger causality and conditional Granger causality are developed in detail, with partic- ular 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 physiolog- ically interpretable and yield new insights into the dynamical organization of large-scale oscillatory cortical networks. 17.1 Introduction In neuroscience, as in many other fields of science and engineering, signals of interest are often collected in the