统计与信息论坛

在复杂的金融市场中，高阶矩(偏度和峰度)包含了资产收益率的有效信息，可以更好地刻画极端事件的发生，且好坏波动率会对未来波动率的预测产生非对称影响。因此，在双成分Realized-GARCH(RGARCH)模型的基础上，纳入时变高阶矩，并在短期方程中引入好坏波动率，提出基于好坏波动率的时变高阶矩双成分RGARCH(双成分RGARCH-RS-SK)模型，该模型充分利用了高阶矩信息，能够更全面地捕捉资产收益率的尖峰厚尾和好坏波动率所表现出的异质性。将所构建模型应用于深证综指，实证和稳健性检验结果显示：(1)所提模型能更全面地刻画波动率存在的非对称性、高阶矩的时变性和“偏态、尖峰厚尾”等特征，拥有出色的拟合和预测效果；(2)依据模型所得VaR是良好的分位数估计，且VaR和ES预测值均通过了统计有效性和损失函数两方面的检验，能更灵活地测度市场风险。基于上述研究结果，将时变高阶矩、好坏波动率和双成分结构相结合可以更准确地预测市场波动率和风险值，促进国家经济稳定发展和风险管理。

In complex financial markets, higher-order moments(skewness and kurtosis) contain valuable information about asset returns and can better characterize the occurrence of extreme events.Additionally, good and bad volatility exert asymmetric effects on future volatility predictions.Therefore, by incorporating time-varying higher-order moments into the two-component Realized-GARCH(RGARCH) model and introducing good and bad volatility into the short-term equation, a time-varying higher-order moment two-component RGARCH(RGARCH-RS-SK) model based on good and bad volatility is proposed.The model fully utilizes the information from higher-order moments and is capable of more comprehensively capturing the features of asset return distributions, such as spikes, heavy tails, and the heterogeneity indicated by good and bad volatility.It is further applied to the Shenzhen Composite Index, the empirical and robustness tests indicate that, the proposed model effectively captures the asymmetry of volatility, the time-varying nature of higher-order moments, and characteristics such as “skewness, spikes, and heavy tails”, demonstrating excellent fitting and forecasting performance.The Value at Risk(VaR) obtained from the proposed model serves as a good quantile estimate, and both VaR and Expected Shortfall(ES) predictions pass the tests of statistical validity and loss function, allowing for more flexible measurement of market risk.These findings suggest that integrating time-varying higher-order moments, good and bad volatility, and a two-component structure can more accurately predict market volatility and risk values, supporting national economic stability and risk management.