This research proposes a new class of RES-CAViaR (conditional autoregressive value-at-risk) models, that incorporate daily realized volatility and expected shortfall (ES) to forecast VaR and ES simultaneously. We further consider weekly and monthly realized volatilities in the proposed model to approximate a long-memory process. We employ the Bayesian adaptive Markov chain Monte Carlo approach to estimate all unknown parameters and to jointly predict daily VaR and ES over a 4-year out-of-sample period including the COVID-19 pandemic. Our results show that the realized CAViaR-type models outperform in terms of three backtests, four loss-function criteria, and ES measurement at the 1% level.

本研究提出了一类新的 RES-CAVIaR（条件自回归风险价值）模型，该模型结合了每日实际波动率和预期短缺 (ES) 来同时预测 VaR 和 ES。我们进一步考虑了所提出模型中每周和每月实现的波动性，以近似一个长记忆过程。我们采用贝叶斯自适应马尔可夫链蒙特卡罗方法来估计所有未知参数，并在包括 COVID-19 大流行在内的 4 年样本外期间联合预测每日 VaR 和 ES。我们的结果表明，实现的 CAVIaR 类型模型在三个回测、四个损失函数标准和 1% 水平的 ES 测量方面表现出色。