大维数据的动态条件协方差阵的估计及其应用

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。本文将主成分和门限方法有效的结合，应用到DCC模型的估计中，提出了基于主成分正交补门限方法的DCC模型（poetDCC）。poetDCC模型主要通过前K个主成分来刻画高维动态条件协方差阵的信息，然后将门限函数应用在矩阵的正交补中，有效的降低了数据的维度并剔除了噪声的影响。通过模拟和实证研究发现：较DCC模型而言，poetDCC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 Study on the Dynamic Conditional Covariance of Large Dimensional Data

High dimensional data poses great challenges to the traditional estimation of covariance, we can’t ignore the influence of data dimension and noise. This paper combines the principal components and thresholding method effectively and applies them to the estimation of DCC model. The poetDCC model is then proposed which is based on the principal orthogonal complement thresholding method. It characterizes the information of large dynamic conditional covariance mainly through the first K principal components, and 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 poetDCC model significantly improves the efficiency of estimation and prediction of large matrix and investors obtain higher returns and economical welfare when the poetDCC model is applied in portfolio.