基于Tlasso的大维协方差矩阵估计及其应用

Tlasso-based Large Dimensional Covariance Matrix Estimation and Its Application

金融数据的大维度性、高度正相关性及非正态性给投资组合中协方差矩阵的估计带来了巨大挑布,并借助l1惩罚项来获得大维逆协方差矩阵的稀疏估计。实证结果表明,相对于等权重模型、样本协方差模型及Glasso模型,Tlasso模型能显著提高大维协方差矩阵的估计效率,并选出最佳的投资组合。

The large dimensionality,highly positive correlation and non-normality of financial data bring great challenges to the estimation of covariance matrix in the portfolio.To solve this problem,the paper proposes a data-driven Tlasso portfolio model.The model assumes that the return on assets obeys multivariate t distribution,and obtains the sparse estimation of the large dimensional inverse covariance matrix by means of l1 penalized term.The empirical results show that compared with the equal-weight model,sample covariance model and Glasso model,the Tlasso model significantly improves the estimation efficiency of large dimensional covariance matrix,and can select the best portfolio.