On variable ordination of modified Cholesky decomposition for estimating time‐varying covariance matrices

Estimating time‐varying covariance matrices of the vector of interest is challenging both computationally and statistically due to a large number of constrained parameters. In this work, we consider an order‐averaged Cholesky‐log‐GARCH (OA‐CLGARCH) model for estimating time‐varying covariance matrices through the orthogonal transformations of the vector based on the modified Cholesky decomposition. The proposed method is to transform the vector at each time as a linear transformation of uncorrelated latent variables and then to use simple univariate GARCH models to model them separately. But the modified Cholesky decomposition relies on a given order of variables, which is often not available, to sequentially orthogonalize the variables. The proposed method develops an order‐averaged strategy for the Cholesky‐GARCH method to alleviate the effect of order of variables. The merits of the proposed method are illustrated through simulations and real‐data studies.