Bayesian Network structural learning in multivariate time series

Structural learning of Bayesian network is usually fulfilled by the expert knowledge, whenever available, or by some efficient algorithmic procedures. Despite the vast literature on structural learning, still little has been done specifically aimed at the multivariate time series modeling. We suggest a testing procedure able to learn the DAG structure whose vertex set only consists of the components of a stationary vector autoregressive VAR(p) model. The proposal procedure follows a constraint-based approach by using a test between blocks of variables. The class of tests proposed is based on multivariate ranks of distances and it is asymptotically distribution-free under very mild assumptions on the noise.