Advances in the various realized GARCH models have proven effective in taking account of the bias in realized volatility (RV) introduced by microstructure noise and non-trading hours. They have been extended into nonlinear or long-memory patterns, including the realized exponential GARCH (EGARCH), realized heterogeneous autoregressive GARCH (HAR-GARCH), and realized threshold GARCH (TGARCH) models. These models with skew Student’s t-distribution are applied to quantile forecasts such as Value-at-Risk and expected shortfall of financial returns as well as volatility forecasting. Parameter estimation and quantile forecasting are built on Bayesian Markov chain Monte Carlo sampling methods. Backtesting measures are presented for both Value-at-Risk and expected shortfall forecasts and employ two loss functions to assess volatility forecasts. Results taken from the S&P500 in the U.S. market with approximately 5-year out-of-sample periods covering the COVID-19 pandemic period are reported as follows: (1) The realized HAR-GARCH model performs best in respect of violation rates and expected shortfall at the 1% and 5% significance levels. (2) The realized EGARCH model performs best with regard to volatility forecasts.

事实证明，各种已实现 GARCH 模型的进步在考虑微观结构噪声和非交易时间引入的已实现波动率 (RV) 偏差方面是有效的。它们已扩展到非线性或长记忆模式，包括实现的指数 GARCH (EGARCH)、实现的异构自回归 GARCH (HAR-GARCH) 和实现的阈值 GARCH (TGARCH) 模型。这些具有偏学生 t 分布的模型适用于分位数预测，例如风险价值和预期财务回报缺口以及波动性预测。参数估计和分位数预测建立在贝叶斯基础上马尔可夫链蒙特卡罗采样方法。针对风险价值和预期缺口预测提出了回溯测试措施，并采用两个损失函数来评估波动性预测。取自美国市场 S&P500 的结果，大约 5 年样本外期间涵盖了 COVID-19 大流行期间： (1) 实现的 HAR-GARCH 模型在违规率和预期方面表现最佳1% 和 5%显着性水平上的不足。(2) 实现的 EGARCH 模型在波动性预测方面表现最佳。