An Efficient Approach to Graphical Modelling of Time Series

TL;DR

This paper introduces a computationally efficient method for graphical modeling of multivariate Gaussian time series, significantly reducing computation time while maintaining statistical power, and enabling parallel processing.

Contribution

It reformulates Matsuda's approach into a multiple hypothesis testing framework, achieving faster computation and parallelizability without sacrificing accuracy.

Findings

Reduces computation time by a factor of p^2

Maintains or improves statistical power

Enables parallel processing for large p

Abstract

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.