大维数据背景下金融协方差阵的估计及应用

Estimation and application study on the financial covariance matrix of large dimensional data

协方差阵在投资组合和风险管理中扮演着重要角色,但是大维数据给传统的协方差阵估计方法带来了巨大挑战.本文将改进的乔列斯基分解和惩罚函数等非参数方法应用到DCC模型的估计中,提出了非参数DCC模型(NPDCC).NPDCC模型首先通过改进的乔列斯基分解方法,将DCC模型估计中复杂的协方差阵估计问题转化为一系列的回归模型,然后通过引入惩罚函数,将一些回归系数压缩为零,解决了维数诅咒问题,使得大维动态条件协方差阵的估计成为可能.通过模拟和实证研究发现:较DCC模型而言,NPDCC模型明显提高了大维协方差阵的估计和预测效率;并且将其应用在投资组合时,投资者获得了更高的投资收益和经济福利.

Covariance matrix plays an important role in portfolio and risk management. However, large dimensional data brings great challenges to the traditional estimation of covariance. In this paper, we apply the modified Cholesky decomposition and penalty function to the estimation of DCC model, and propose a nonparametric DCC （NPDCC） model. Firstly, by using modified cholesky decomposition, the nonparametric DCC （NPDCC） model transforms the problem of estimating complex covariance matrix into a series of regression models. By introducing the penalty function, some regression coefficients are then compressed to 0, so as to solve the problem of dimension curse. Through simulation and empirical studies, it is found that nonparametric DCC （NPDCC） model significantly improves the efficiency of estimation and prediction of large matrix; it is also found that, investors obtain higher returns and economical welfare when the NPDCC model is applied in portfolio.