基于因子收缩方法的高维协方差估计

High-Dimensional Covariance Estimation Based on Factor Shrinkage Method

高维协方差矩阵在经济、金融、生物等众多领域中有着广泛应用.基于收缩估计模型,构造样本协方差矩阵与因子模型协方差矩阵的凸线性组合,通过对因子模型的改进来提高模型估计精度.在构造因子模型时,引入因子选择准则(pc_(p3)(k))来确定因子个数:在确定最优权重α时,使用基于MSE(S)分解的思想求解.通过数据验证发现,相较于传统方法,提升了协方差矩阵估计精确性;在构造投资组合模型时,也可以有效降低投资风险.

High dimensional covariance matrix is widely used in many fields such as economy,finance and biology.Based on the contraction estimation model,this paper constructs the convex linear combination of sample covariance matrix and factor model covariance matrix,and improves the accuracy of model estimation by improving the factor model.When constructing factor model,factor selection criterion(pc_(p3)(k)) is introduced to determine the number of factors.To determine the optimal weight α,M SE(S)decomposition is used to solve the problem.Through data verification,it is found that the proposed method improves the accuracy of covariance matrix estimation compared with the traditional method.The proposed method can also effectively reduce the investment risk when constructing the portfolio model.