An Efficient Approach to Graphical Modeling of Time Series

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(p²) 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.