Extreme conditional tail risk inference in ARMA–GARCH models
研究了ARMA-GARCH模型下极端条件风险价值(CVaR)和条件预期亏损(CES)的估计方法，通过极值理论推导渐近性质，模拟和实证验证了方法的有效性，适用于金融资产尾部风险预测。
In this study, we investigate the estimation of extreme conditional Value-at-Risk (CVaR) and conditional Expected Shortfall (CES) within the framework of ARMA-GARCH models, where innovations are assumed to follow a Pareto-type tail distribution and have no finite fourth moments. Building on the two-stage self-weighted estimation procedure proposed by He et al. (2022) , we develop a robust methodology for forecasting extreme CVaR and CES. Using extreme value theory, we derive a unified asymptotic theory for the extreme CVaR and CES estimators. Through comprehensive simulation studies, we evaluate the performance of our approach and compare it with several recently proposed estimators in the literature. Additionally, we apply our methodology to forecast extreme CVaR and CES for daily negative log-returns (i.e., losses) of four financial assets, demonstrating its practical applicability in financial risk management.