Estimating High Dimensional Covariance Matrices and its Applications

Jushan Bai

and

Shuzhong Shi

Estimating covariance matrices is an important part of portfolio selection,
risk management, and asset pricing. This paper reviews the recent development in estimating high dimensional covariance matrices, where the number of variables can be greater than the number of observations. The limitations of the sample covariance matrix are discussed. Several new approaches are presented, including the shrinkage method, the observable and latent factor method, the Bayesian approach, and the random matrix theory approach. For each method, the construction of covariance matrices is given. The relationships among these methods are discussed.