Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk
分位数图模型：预测、条件独立与系统性风险应用AI 解读 ↓
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分位数图模型：预测、条件独立与系统性风险应用
- 研究问题
- 在变量数量很大、冲击非高斯且非可分时，如何描述不同分位数处的条件独立和预测依赖，并刻画金融尾部关联？
- 方法与思路
- 作者区分条件独立与预测两类分位数图模型，使用高维惩罚分位数方法估计，并构造统一收敛结果和同时置信区域。
- 材料陈述的贡献
- 摘要称建立两类图模型的估计推断理论，其中预测模型允许误设；所得尾部风险网络可用于度量系统性风险贡献。
- 阅读关注点
- 应核对两类图的边各自代表什么、条件独立识别所需假设，以及同时推断与尾部风险贡献指标的具体构造。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未列明完整条件，统计依赖图不能直接解释为因果传播网络。
原文摘要
We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by evaluating the distributional dependence structure at each quantile index. As such, CIQGMs can be used for validation of the graph structure in the causal graphical models (\cite{pearl2009causality, robins1986new, heckman2015causal}). One main advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. PQGMs characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. Because of QGMs' ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements. We develop estimation and inference methods for QGMs focusing on the high-dimensional case, where the number of variables in the graph is large compared to the number of observations. For CIQGMs, these methods and results include valid simultaneous choices of penalty functions, uniform rates of convergence, and confidence regions that are simultaneously valid. We also derive analogous results for PQGMs, which include new results for penalized quantile regressions in high-dimensional settings to handle misspecification, many controls, and a continuum of additional conditioning events.