رابطه بین علیت فرایندهای تصادفی و بلوک های صفر ماتریس انتقال نوآوری مشترک

We consider output processes which are realizable by stochastic linear time-invariant (LTI) systems. Such processes can always be realized by LTI systems in forward innovation form, and we study the transfer matrices of such LTI realizations. We show that such a transfer matrix is consistent with an acyclic directed graph if and only if the edges of this graph represent Granger-causality relations among the components of the output process. By consistency we mean that if there is no edge between two vertices of the graph, then the corresponding block of the transfer matrix is zero. Under this assumption, conditional Granger non-causality between the components of the process is equivalent with a zero block in the transfer matrix.