基于贝叶斯框架的协方差矩阵估计模型研究

Research on Covariance Matrix Estimation Model Based on a Bayesian Framework

摘要: 为了更好地估计股票收益协方差矩阵，提出了一种新的基于贝叶斯框架的协方差矩阵估计模型。该模型将Black-Litterman思想推广到协方差矩阵的估计中，通过挖掘金融文本信息构建投资者情绪指标，运用随机森林回归方法生成投资者主观观点矩阵。在传统协方差矩阵估计模型中加入投资者观点的先验信息，结合市场历史经验数据给出协方差矩阵的先验分布。利用贝叶斯方法得到协方差矩阵的最大后验形式，同时考虑协方差矩阵实值矩阵中存在的非负结构，提出了一种联合考虑投资者信息与非负结构的协方差矩阵估计的最大后验模型。运用投影梯度法求解该模型，并通过对比实验，从模拟数据与实际市场数据两部分验证了算法的有效性和模型的优越性。

Abstract: To enhance the estimation of the covariance matrix for stock returns, a new estimation model based on a Bayesian framework is presented. This model extends the idea of the Black-Litterman approach to estimate the covariance matrix. It builds investor sentiment indicators by mining financial text information and forms an investor subjective view matrix using the random forest regression method. The prior information of investors’ views is incorporated into the traditional covariance matrix estimation model, and the prior distribution of the covariance matrix is obtained by combining historical market data. The Bayesian method is utilized to obtain themaximum posterior form of the covariance matrix, while also considering the non-negative structure inherent in the real-valued matrix of the covariance matrix. The projected gradient method is employed to solve the model, and the effectiveness of the algorithm and the superiority of the model are verified on simulated data and real market data.