Conditional independence graphs for multivariate autoregressive models by convex optimization: Efficient algorithms

Abstract

In this paper, we introduce novel algorithms for inferring the conditional independence graph of a vector autoregressive (VAR) process. As part of this work, we derive the renormalized maximum likelihood criterion for VAR-order selection and prove its consistency. Finding the graphical model for VAR reduces to identify the sparsity pattern of the inverse of its spectral density matrix; we show how efficient implementations of convex optimization algorithms can be used to solve this problem; in our approach, the high-sparsity assumption is not needed. We conduct experiments with simulated data, air pollution data and stock market data for demonstrating that our algorithms are faster and more accurate than similar methods proposed in the previous literature. Keywords: Vector autoregressive model, conditional independence, convex optimization, renormalized maximum likelihood, maximum entropy.