基于动态收缩法的大维协方差阵的估计及其应用

Estimation and Application of Large Dimensional Covariance Matrix Based on Dynamic Shrinkage Method

文章将单因子协方差阵和样本协方差阵相结合,通过对它们进行最优加权平均,提出了新的协方差阵估计方法——动态加权收缩估计量(DWS)。该估计量一方面通过选择最优的权重来平衡协方差阵估计的偏差和误差;另一方面估计的是大维数据的动态协方差阵,在估计过程中考虑了前期信息的影响。通过模拟和实证研究发现:较传统的协方差阵估计方法而言,DWS估计量明显提高了大维协方差阵的估计效率;并且将其应用在投资组合时,投资者获得了更高的收益和经济福利。

Combining the single factor covariance matrix and the sample covariance matrix, this paper presents a new covariante matrix estimation method--dynamic weighted shrinkage estimator （DWS） by taking the optimal weighted average. The new estimator trades off the bias and errors of the covariance matrix estimation by selecting the optimal weights. And at the same time, it estimates the dynamic eovariance matrix for high dimensional data and considers the influence of prior information on covariance matrix estimation. Simulation and empirical studies demonstrate that DWS estimator significantly improves the efficiency of estimation and prediction of large matrix compared with the traditional eovariance matrix estimation approach, and investors obtain higher returns and more economical welfare when the DWS estimator is applied to the investment portfolio.