Should We Augment Large Covariance Matrix Estimation with Auxiliary Network Information?

In this paper, we propose two novel frameworks to incorporate auxiliary information about interconnections among entities (i.e., network information) into the estimation of large covariance matrices. The current literature either completely ignores this kind of network information (e.g., thresholding and shrinkage) or imposes some very restrictive network structure that limits the application (e.g., banding). In the era of big data, we have easy access to auxiliary network information about these interconnections. Depending on the features of the auxiliary network information at hand and the structure of the covariance matrix, we provide two different frameworks correspondingly —the Network Guided Thresholding and the Network Guided Banding. We show that both Network Guided estimators have optimal convergence rates over a larger class of sparse covariance matrices. Simulation studies indicate that these estimators generally outperform other purely statistical methods, particularly when the true covariance matrix is sparse and the auxiliary network provides reliable information. Empirically, we apply our methods to estimate the covariance matrix of asset returns using various forms of auxiliary network data to construct the global minimum variance (GMV) and Mean-Variance Optimal (MVO) portfolios.