This paper considers the specification of covariance structures with tail estimates. We focus on two aspects: (i) the estimation of the VaR-CoVaR risk matrix in the case of larger number of time series observations than assets in a portfolio using quantile predictive regression models without assuming the presence of nonstationary regressors and; (ii) the construction of a novel variable selection algorithm, so-called, Feature Ordering by Centrality Exclusion (FOCE), which is based on an assumption-lean regression framework, has no tuning parameters and is proved to be consistent under general sparsity assumptions. We illustrate the usefulness of our proposed methodology with numerical studies of real and simulated datasets when modelling systemic risk in a network.

翻译：本文考虑了具有尾部估计的协方差结构设定问题。我们聚焦于两个方面：(i) 在资产数量多于时间序列观测值的情况下，使用分位数预测回归模型估计VaR-CoVaR风险矩阵，且不假设存在非平稳回归变量；(ii) 构建一种新颖的变量选择算法，称为“基于中心性排除的特征排序”（FOCE），该算法基于假设精简的回归框架，无需调整参数，并在一般稀疏性假设下被证明具有一致性。我们通过真实和模拟数据集的数值研究，说明了所提方法在建模网络系统性风险中的实用性。