A causal vector autoregressive (CVAR) model is introduced for weakly stationary multivariate processes, combining a recursive directed graphical model for the contemporaneous components and a vector autoregressive model longitudinally. Block Cholesky decomposition with varying block sizes is used to solve the model equations and estimate the path coefficients along a directed acyclic graph (DAG). If the DAG is decomposable, i.e., the zeros form a reducible zero pattern (RZP) in its adjacency matrix, then covariance selection is applied that assigns zeros to the corresponding path coefficients. Real-life applications are also considered, where for the optimal order p≥1 of the fitted CVAR(p) model, order selection is performed with various information criteria.