An edge exclusion test for graphical modeling of multivariate time series

We consider the problem of inferring the conditional independence graph of a stationary multivariate Gaussian time series. A p-variate Gaussian time series graphical model associated with an undirected graph with p vertices is defined as the family of time series that obey the conditional independence restrictions implied by the edge set of the graph. In some existing methods, partial coherence has been used as a test statistic for graphical model selection. To test inclusion/exclusion of a given edge in the graph, the test is applied at distinct frequencies, requiring multiple tests, leading to a loss in test power. The nonparametric methods of Matsuda (2006) and Wolstenholme and Walden (2015) use the Kullback-Leibler divergence measure to define a test statistic which does not need multiple testing to test between two competing models. In this paper, we propose a generalized likelihood ratio based edge exclusion test statistic that also does not need multiple testing. It is computationally significantly faster than the methods of Matsuda and Wolstenholme-Walden, and simulations show that we achieve comparable power levels.