  A method for selecting a graphical model for $p$-vector-valued stationary
Gaussian time series was recently proposed by Matsuda and uses the
Kullback-Leibler divergence measure to define a test statistic. This statistic
was used in a backward selection procedure, but the algorithm is prohibitively
expensive for large $p.$ A high degree of sparsity is not assumed. We show that
reformulation in terms of a multiple hypothesis test reduces computation time
by $O(p^2)$ and simulations support the assertion that power levels are
attained at least as good as those achieved by Matsuda's much slower approach.
Moreover, the new scheme is readily parallelizable for even greater speed
gains.
