Relationship between Granger non-causality and graph structure of   state-space representations
  In this paper we present an equivalent form of Granger noncausality in state space representation. As a generalization of this result, necessary and sufficient conditions are provided for an output process to admit a particular minimal coordinated state space representation. 
M. Jozsa, M. Petreczky, and M. K. Camlibel
math.OC