Large covariance matrix estimation with factor-assisted variable clustering

Abstract: This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse error covariance matrix after taking out common factors may be invalid for many financial applications. Our formulation postulates a latent model-based error cluster structure after removing observable factors, which not only leads to more interpretable cluster patterns but also accounts for non-sparse cross-sectional correlations among the variable-specific residuals. Our method begins with using least-squares to estimate the factor loadings, followed by identifying the latent cluster structure by thresholding the scaled covariance difference measures of residuals. A novel ratio-based criterion is introduced to determine the threshold parameter when performing the developed clustering algorithm. We then establish the cluster recovery consistency of our method and derive the convergence rates of our proposed covariance matrix estimators under different norms. Finally, we demonstrate the superior finite sample performance of our proposal over the competing methods through both extensive simulations and a real data application on minimum variance portfolio.