Abstract: 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.

Key words: realized volatility, dynamic estimation errors, high-frequency data, jump behavior, leverage effect