基于高维数据的改进CCC-GARCH模型的估计及应用

高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使传统的CCCGARCH模型估计起来较为困难。将主成分和门限方法有效结合,应用到CCC-GARCH模型的估计中,提出基于主成分正交补门限方法的CCC-GARCH模型(PTCCC-GARCH)。PTCCC模型主要通过前K个最优主成分来刻画大维协方差阵的信息,并通过门限函数以剔除噪声的影响。通过模拟和实证研究发现:较CCCGARCH模型而言,PTCCC-GARCH模型明显提高了高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。

Estimation and Application of the Improved CCC-GARCH Model of High Dimensional Data

High dimensional data poses great challenges to the traditional estimation of covariance,it is difficult to estimate the traditional CCC-GARCH model because of the influence of data dimension and noise.We combine the principal components and thresholding method effectively and applies them to the estimation of CCC-GARCH model.The PTCCC-GARCH model is then proposed which is based on the principalorthogonal complement thresholding method.It characterizes the information of large covariance mainly through the first K principal components, the thresholding function is then applied in the orthogonal complement of matrix,so as to reduce data dimensions and exclude the noise effects effectively. Through simulation and empirical studies,it is found that PTCCC-GARCH model significantly improves the efficiency of estimation and prediction of large matrix and investors obtain higher returns and economical welfare when the PTCCC-GARCH model is applied in portfolio.