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This paper addresses the problem of inferring circulation of informationbetween multiple stochastic processes. We discuss two possible frameworks inwhich the problem can be studied: directed information theory and Grangercausality. The main goal of the paper is to study the connection between thesetwo frameworks. In the case of directed information theory, we stress theimportance of Kramer's causal conditioning. This type of conditioning isnecessary not only in the definition of the directed information but also forhandling causal side information. We also show how directed informationdecomposes into the sum of two measures, the first one related to Schreiber'stransfer entropy quantifies the dynamical aspects of causality, whereas thesecond one, termed instantaneous information exchange, quantifies theinstantaneous aspect of causality. After having recalled the definition ofGranger causality, we establish its connection with directed informationtheory. The connection is particularly studied in the Gaussian case, showingthat Geweke's measures of Granger causality correspond to the transfer entropyand the instantaneous information exchange. This allows to propose aninformation theoretic formulation of Granger causality.

Relating Granger causality to directed information theory for networks of stochastic processes