  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 $p\ge 1$ of the
fitted CVAR$(p)$ model, order selection is performed with various information
criteria.
