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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.
The covariance matrix plays an important role in the portfolio and risk management, but the large dimensional data poses a great challenge to the traditional covariance matrix estimation method.In this paper, the non-parametric methods such as the improved Cholesky decomposition and penalty function are applied In the estimation of DCC model, a non-parametric DCC model (NPDCC) is proposed.NPDCC model firstly transforms the complex covariance matrix estimation problem in DCC model estimation into a series of regression models through the improved Cholesky decomposition method, Then by introducing a penalty function, some regression coefficients are reduced to zero, which solves the curse of dimensionality and makes it possible to estimate the covariance matrix of the large-dimensional dynamic conditions. The simulation and empirical studies show that compared with the DCC model, the NPDCC model is obviously Which improves the estimation and prediction efficiency of the covariance matrix of large dimension. And when it is applied to the portfolio, investors get higher return on investment and economic benefits.