Covariance Matrix Regression Models

• Activity Number: 560
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Isolated Statisticians
• Author(s): Tao Zou*+ and Wei Lan
• Companies: Peking University and Southwestern University of Finance and Economics, China
• Keywords: High Dimensional Data ; Covariance Matrix Estimation ; Regression

Abstract

We propose covariance matrix regression models that parameterize the high dimensional covariance matrix in order to (i) obtain the estimator of the covariance matrix; and (ii) utilize auxiliary information to describe the structure of the covariance. We show that the model not only has a faster convergence rate for the covariance matrix estimation, compared with traditional methods, but also provides an explanation about how the auxiliary information contributes to the covariance structure, which are very applicable in areas of spatial econometrics, social network studies and financial portfolio management. Simulation experiments were conducted to mimic the reality and to confirm the theoretical properties of the estimators concerned. We also implement dynamic financial portfolio management in the Chinese stock market based on our estimation.