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 timevarying 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.

中文翻译：

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用于估计时变协方差矩阵的修正 Cholesky 分解的变量排序

由于大量约束参数，估计感兴趣向量的时变协方差矩阵在计算和统计上都具有挑战性。在这项工作中，我们考虑了一个顺序平均 Cholesky-log-GARCH (OA-CLGARCH) 模型，用于通过基于改进的 Cholesky 分解的向量的正交变换来估计时变协方差矩阵。所提出的方法是每次将向量变换为不相关潜在变量的线性变换，然后使用简单的单变量GARCH模型分别对其进行建模。但是修改后的 Cholesky 分解依赖于给定的变量顺序，这通常是不可用的，以顺序正交化变量。所提出的方法为 Cholesky-GARCH 方法开发了一种顺序平均策略，以减轻变量顺序的影响。通过模拟和实际数据研究说明了所提出方法的优点。