Should we augment large covariance matrix estimation with auxiliary network information?

Abstract

This paper uses the auxiliary network information, observed in addition to the original sample, to infer latent network structures in the population correlation matrix and thus improve high-dimensional covariance matrix estimation. Building on estimated Location Indicator and Relative Importance matrices, we propose two Network-Guided estimators. Network-Guided Thresholding uses auxiliary network data to regularize the large and small elements in the sample covariance matrices differentially, delivering a faster convergence rate over a more general class of sparse covariance matrices when auxiliary information is informative. Network-Guided Banding extends the banding estimators to allow for data without a natural ordering, using the relative importance of elements indicated by the auxiliary datasets to construct a neighbor ordering, which can achieve the optimal convergence rate that would be infeasible without the auxiliary network information. Extensive simulation studies show robust finite-sample gains of the proposed Network-Guided estimators over existing benchmark methods. The proposed methods also deliver superior out-of-sample performance relative to the established baseline models in the empirical application of constructing Global Minimum Variance (GMV) and Mean-Variance Optimal (MVO) portfolios in the Chinese stock market with various sources of auxiliary network information, including analyst co-coverage, news co-mentions, and industry classifications.