  Graphical interaction models have become an important tool for analysing
multivariate time series. In these models, the interrelationships among the
components of a time series are described by undirected graphs in which the
vertices depict the components while the edges indictate possible dependencies
between the components. Current methods for the identification of the graphical
structure are based on nonparametric spectral stimation, which prevents
application of common model selection strategies. In this paper, we present a
parametric approach for graphical interaction modelling of multivariate
stationary time series. The proposed models generalize covariance selection
models to the time series setting and are formulated in terms of inverse
covariances. We show that these models correspond to vector autoregressive
models under conditional independence constraints encoded by undirected graphs.
Furthermore, we discuss maximum likelihood estimation based on Whittle's
approximation to the log-likelihood function and propose an iterative method
for solving the resulting likelihood equations. The concepts are illustrated by
an example.
