本文设波动率的估计误差服从异方差假定，在对已实现波动率进行建模时，根据方差变化来设定模型的自回归系数，构建基于高频数据的HARQ（F）模型。在此基础上，考虑中国股市波动的跳跃行为及杠杆效应，先后构建了HARQ（F）-CJ模型和LHARQ（F）-CJ模型，以改善波动率模型的拟合效果和预测能力。本文假设，当期已实现波动率或其连续成分的估计误差的方差越大，它对未来真实波动率的解释力度则越差，因而其对应系数越小。对上证综合指数近15年的五分钟高频数据进行实证研究发现，基于估计误差异方差假定的动态系数能够提高已实现波动率模型的拟合效果和预测能力。其中，对日回归系数进行基于估计误差方差的动态调整是模型改进的关键。同时考虑中国股市波动的跳跃行为及杠杆效应的LHARQ-CJ模型在所有模型中表现最优。
As high-frequency data is widely used in forecasting stock volatility, we propose a new family of easy-to-implement models based on realized volatility, which is constructed from the summation of the squared high-frequency intraday returns. In this paper, the estimation error of the realized volatility is assumed to obey the assumption of heteroscedasticity. When modeling the volatility of stock market, we set the autoregressive coefficients of the model according to the change of estimation errors' variances and get HARQ (F) model. In the meantime, we propose HARQ (F)-CJ model and LHARQ (F)-CJ model in combination with the jump behavior and leverage effect of Chinese stock market volatility to improve the fitness and predictive power of the realized volatility model. We suppose, the larger the estimation error's variance of the realized volatility or the continuous component in the current period, the worse its interpretation of the latent volatility in the future,and the smaller the corresponding coefficient is. Through an empirical study on the high-frequency data of the Shanghai Composite Index from December 31st, 2015 to January 2nd, 2001, we find that based on the assumption of heteroscedasticity in the estimation errors, dynamic coefficients can improve the fitness and the predictive power of the realized volatility model. Above all, the dynamic adjustment of daily regression coefficient based on estimation error variance is the key to improve the fitness and predictive power of the model. The LHARQ-CJ model in combination with both the jump behavior and the leverage effect of the Chinese stock market is considered to show the best performance in all related models. Finally, this research has made its contribution in modeling and forecasting Chinese stock volatility with dynamic estimation errors and dynamic autoregressive coefficients.
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