Generalization of Granger Causality in Continuous Time

Abstract: The paper considers a statistical concepts of causality in continuous time between flows of information and between stochastic processes which is based on Granger’s definitions of causality. More precisely, we will see how conditional orthogonality and conditional independence can serve as a basis for a general probabilistic theory of causality for both stochastic processes and single events. These results are motivated by causality relationship between filtrations ”(Gt) is a cause of (Et) within (Ft)” and which is based on Granger’s definition of causality. Also, we consider causality relationships between s-fields (filtrations) associated by stopping times, which are applicable to the stopped processes (see Petrovic et al. 2016). Then we give some basic properties of causality up to some stopping time.