Graphical models have become an important tool for analyzing multivariate data. While originally the interpretation of graphical models has been restricted to conditional independences between variables there has recently been growing interest in graphical models as a general framework for causal modelling and inference in experimental and observational studies. In this talk we discuss two approaches for the identification of cause-effect relationships from multivariate time series data. Both approaches exploit the fact that an effect cannot precede its cause in time for causal inference.
We first describe partial correlation graphs as a generalization of concentration graphs for time-dependent data and show how additional information on the lags between correlated variables can be used to retrieve the ordering of the variables. We then present a new class of graphs which visualize the dynamic relationships between the components of a multivariate process. In these graphs, the vertices represent the components of the process and arrows connecting the vertices correspond to Granger causality. Further the contemporaneous dependence structure of the process is represented by undirected lines between the vertices. These graphs are related to the partial correlation graphs by simple moralization rules. We further introduce a pathwise global causal Markov property and discuss the consequences for causal inference.
The presented concepts are illustrated by an application from neurophysiology in which functional neural connectivity is identified from simultaneously recorded neural spike trains.