Relationship between Granger non-causality and network graph of state-space representations

In this thesis we study dynamical systems that consist of interconnected subsystems. We address the problem of relating the network of subsystems to statistical properties of the output process of the dynamical system. The considered systems are: linear time invariant state-space (LTI–SS) representation, LTI transfer matrix and general bilinear state-space (GB–SS) representation. The network of subsystems of the dynamical system is represented by a directed graph that we call network graph whose nodes correspond to the subsystems and whose edges correspond to the directed communication between the subsystems. The statistical property of the output process is, in LTI systems, the so-called conditional and unconditional Granger causality and, in GB–SS representation, the so called GB–Granger causality.

The main results of this thesis provide formal relationship between the network of subsystems of a dynamical system and the above-mentioned statistical properties of its output process. The thesis also introduces realization and identification algorithms for constructing the dynamical systems under consideration. The results can be of interest in application in e.g., systems biology, neuroscience, and economics.