在大数据时代, 如何估计高维投资组合的风险是金融机构面临的一大难题. 针对这一难题, 文章主要做了两方面研究: 首先, 将非线性收缩法 和QuEST函数应用到BEKK模型中, 提出BEKK-NS模型, 以估计和预测在资产组合中扮演着重要角色的资产协方差阵. 该模型同时适用于估计正态分布和厚尾分布数据的协方差阵, 并且能够很好地解决维数诅咒问题, 提高协方差阵的估计效率. 其次, 构造了基于循环分块bootstrap方法的极限误差$\hat{U}(\alpha )$来评价高维投资组合的风险. 通过模拟和实证研究发现: BEKK-NS模型明显优于BEKK, 将其应用在投资组合时, 降低了组合风险, 使得投资者获得了更高的收益; 并且极限误差$\hat{U}(\alpha )$非常接近于真实的误差, 由其构造的组合风险的置信区间较为精确.

In the era of big data, it is a big challenge for financial institutions to estimate the risk of high dimensional portfolios. This thesis~focused~on~the~following~two~aspects: Firstly, the non-linear shrinkage method and the QuEST function are applied to the BEKK model, and a new covariance matrix estimation and prediction model --- BEKK-NS is proposed to estimate and predict the covariance matrix that plays an important role in the portfolio. The model not only can be used to estimate the covariance matrix of the normal distribution and the heavy tailed distribution, but also can solve the curse of dimensionality and improve the efficiency of the covariance matrix; Secondly, the limit errors $\hat{U}(\alpha )$ which is based on block bootstrap method is constructed to evaluate the risk of the large portfolio. It is found through simulation and empirical researches that the BEKK-NS model is better than the BEKK model, investors can reduce risk and get higher returns when the BEKK-NS model is applied in portfolio; Moreover, the limit error constructed in this paper is very close to the real error, and the confidence interval of the portfolio risk constructed by $\hat{U}(\alpha )$ is more accurate.