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：本文研究基于尾部估计的协方差结构设定问题。我们重点关注两个方面：（i）在时间序列观测数量大于投资组合资产数量的场景下，使用分位数预测回归模型估计VaR-CoVaR风险矩阵，且无需假设存在非平稳回归变量；（ii）构建一种新型变量选择算法——即“中心性排除特征排序”（FOCE），该算法基于无假设回归框架，无需调优参数，并在一般稀疏性假设下被证明具有一致性。我们通过对真实与模拟数据集进行数值研究，展示了所提方法在建模网络系统性风险中的实用性。