Estimation of Large Covariance Matrices with Mixed Factor Structures

We extend the Principal Orthogonal complEment Thresholding (POET) framework introduced by Fan et al. (2013) to estimate large static covariance matrices with a "mixed" structure of observable and unobservable common factors, and we call this method the extended POET (ePOET). A stable covariance estimator for large-scale data is developed by combining observable factors and sparsity-induced weak latent factors, with an adaptive threshold estimator of idiosyncratic covariance. Under some mild conditions, we derive the uniform consistency of the proposed estimator for the cases with or without observable factors. Furthermore, several simulation studies show that the ePOET achieves good finite-sample performance regardless of data with strong, weak, or mixed factors structure. Finally, we conduct empirical studies to present the practical usefulness of the ePOET.