统计与管理学院2015年学术报告第24期
【主 题】 Vast Integrated Covariance And Precision Matrix Estimation By Combining Low and High Frequency Data
【报告人】 刘成 博士
武汉大学经济与管理学院
【时 间】 2015年6月19日（星期五）15:30－16:15
【地 点】 上海财经大学统计与管理学院大楼1208室
【语 言】 英文
【摘 要】The integrated covariance matrix (ICM) of financial assets and the inverse of it---integrated precision matrix (IPM), play crucial roles in many financial applications, such as the estimation of the IPM is the foundation of portfolio choice problems. In this paper, we propose new estimators of a vast dimensional ICM and IPM by combining the low and high frequency data and apply our estimator of the IPM on portfolio choice problems. We show that (1) our estimator are positive definite almost surely if the true ICM is so; (2) our estimators perform well for any dimensional ICM---where the dimension p can go to infinity and can even bigger than the frequency of the data; (3) the estimators are asymptotic optimal in the class of estimators which shrinkage the eigenvalues of a sample covariance matrix; (4) the computational speeds of our estimators are quite fast even when p is very large. Advantages of our estimators are demonstrated by extensive simulations and real data analysis.
