Geometric and long run aspects of Granger causality
格兰杰因果的几何与长期性质
This paper extends multivariate Granger causality to take into account the subspaces along which Granger causality occurs as well as long run Granger causality. The properties of these new notions of Granger causality, along with the requisite restrictions, are derived and extensively studied for a wide variety of time series processes including linear invertible processes and VARMA. Using the proposed extensions, the paper demonstrates that: (i) mean reversion in L2 is an…