Granger-causality graphs for multivariate time series

In this paper, we discuss the properties of mixed graphs which visualize causal relationships between the components of multivariate time series. In these Granger-causality graphs, the vertices, representing the components of the time series, are connected by arrows according to the Granger-causality relations between the variables whereas lines correspond to contemporaneous conditional association. We show that the concept of Granger-causality graphs provides a framework for the derivation of general noncausality relations relative to reduced information sets by performing sequences of simple operations on the graphs. We briefly discuss the implications for the identification of causal relationships. Finally we provide an extension of the linear concept to strong Granger-causality. JEL classification: C320