大维协方差阵的估计及其应用  

The Estimation and Application of Large Dimensional Covariance Matrix

作　　者：刘丽萍[1] 王紫萍[1] LIU Li-ping WANG Zi-ping(School of Mathematics and Statistics, Guihou University of Finance and Economics, Guiyang 550025, Chin)

机构地区：[1]贵州财经大学数学与统计学院,贵州贵阳550025

出　　处：《数学的实践与认识》2016年第20期1-9,共9页Mathematics in Practice and Theory

基　　金：贵州省教育厅2015年度普通本科高校自然科学研究项目(黔教合KY字[2015]423);2015年全国统计科学研究项目(2015LY19);国家社会科学基金(16CTJ013)

摘　　要：大维数据给传统的协方差阵估计方法带来了巨大的挑战,数据维度和噪声的影响不容忽视.首先以风险因子为自变量,对股票收益率建立线性回归模型;然后通过引入惩罚函数将取值非常接近的回归系数归为一组,近而来估计大维数据的协方差阵,提出了基于回归聚类算法的分块模型(BM-CAR),模型克服了传统的稀疏协方差阵估计的弊端.通过模拟和实证研究发现:较因子协方差阵估计方法而言,BM-CAR明显提高了大维协方差阵的估计效率;并且将其应用在投资组合时,投资者获得了更高的收益和经济福利.High dimensional data poses great challenges to the traditional estimation of covariance;we can＇t ignore the influence of data dimension and noise.In this paper,we firstly use risk factors as independent variables,and establish a linear regression model of stock returns.Then by introducing the penalty function,we will merge into a set of regression coefficients that are very close,to estimate the covariance matrix of large dimensional data.The BM-CAR is proposed which is based on the clustering algorithm in regression.The model overcomes the disadvantages of traditional sparse covariance matrix.Through simulation and empirical studies,it is found that BM-CAR significantly improves the efficiency of estimation and prediction of large matrix and investors obtain higher returns and economical welfare when the BM-CAR model is applied in portfolio.

关 键 词：回归聚类算法 BM-CAR模型 大维协方差阵 

分 类 号：O212.1[理学—概率论与数理统计]