Causality and Network Graph in General Bilinear State-Space Representations

This article proposes an extension of the well-known concept of Granger causality, called GB-Granger causality. GB-Granger causality is designed to relate the internal structure of bilinear state-space systems and statistical properties of their output processes. That is, if such a system generates two processes, where one does not GB-Granger cause the other, then it can be interpreted as the interconnection of two subsystems: one that sends information to the other, and one which does not send information back.This result is an extension of earlier obtained results on the relationship between Granger causality and the internal structure of linear time-invariant state-space representations.