LAUSR

The estimation of the large and high-dimensional covariance matrix and precision matrix is a fundamental problem in modern multivariate analysis. It has been widely applied in economics, finance, biology, social networks and health sciences. However, the traditional sample estimators perform poorly for large and high-dimensional data. There are many approaches to improve the covariance matrix estimation. The large dynamic conditional correlation model based on the nonlinear shrinkage and its application in portfolio selection attract increasing attention. In the estimation of the unconditional covariance matrix, the graphical lasso is more robust than the nonlinear shrinkage model, and the leptokurtic and fat tail characteristics of the asset returns are also more obvious. This article proposes improved large dynamic covariance matrix estimation based on the graphical lasso models under the multivariate normal distribution (glasso) and $t$ distribution (tlasso), and the corresponding dynamic conditional correlation glasso and tlasso approaches are developed. To verify the effectiveness and robustness of the proposed methods, we conduct simulations and then apply the models to the classic Markowitz portfolio selection problem. Simulations and empirical results show that the combined dynamic conditional correlation glasso and tlasso approaches outperform the current dynamic covariance matrix estimators.