Large covariance estimation using a factor model with common and group-specific factors

This paper proposes a new approach to estimate large covariance matrices using multilevel factor models. In order to further improve the efficiency of the principal orthogonal complement thresholding estimator (PEOT) and the proposed estimators, the generalized least squares (GLS) method is employed to refine the estimation of the factors. A novel approach to identify number of the factors is proposed for facilitating our estimation procedure. We prove the consistency of the covariance matrix estimators and the estimators for number of the factors. Our Monte Carlo simulations show that the proposed estimators have superior properties in finite samples for all different designs, and the efficiency can be improved significantly by using GLS. Finally, we apply our estimators to a dataset consisting of weekly returns of three major stock indexes constituents, and the results suggest that the proposed methods can improve the out-of-sample performances of portfolio optimization.