高频数据下高维协方差阵的RCM算法估计与应用

Large-dimensional covariance matrix estimation and its application with RCM using high frequency data

基于因子模型的估计方法是高频数据下高维协方差矩阵估计的一个重要方向.为了解决行业分类门限法的主观性问题,本文使用RCM算法对剔除了主要成分的残差矩阵进行重新排序并进行分块对角化门限处理.本文首先在数值模拟中设定残差矩阵包含分块对角结构并将其顺序打乱,随后使用RCM算法进行重新排序,结果表明其能够还原乱序残差矩阵中所包含的分块对角结构.基于2015年股灾期间和2018全年的高频数据,本文将预平均法和使用RCM进行分块对角处理的POET方法进行结合,并在实证研究中对包括该估计量在内的多种协方差估计量进行了样本外预测效果的比较.结果显示改进后的估计量具有更好的预测能力,进行含总敞口约束的最小方差组合投资时的日内波动率整体较低.

Factor-based covariance estimation is an important direction of high-frequency and largedimensional covariance estimation.In order to overcome the subjectivity of sector-based block-diagonalizing method,we introduce RCM reordering method to reorder the residual matrix and conduct thresholding under new block-diagonal structure.Firstly,we disorganize the original residual matrix that contains clear block-diagonal structure.Then we use RCM to restore its order and the result shows that RCM can fully restore the latent block-diagonal structure.Next,using high-frequency data of market crash period in.2015 and year 2018,we combine pre-averaging method and RCM-based POET to construct a new covariance estimator.The comparison of this new estimator against the others suggests that the modified factor model and estimator outperform other covariance estimators in terms of predicting the future.Moreover,it also performs well when optimizing the minimum variance portfolio with gross-exposure constraint.