Mix Frequency Realized GARCH Models:the Forecast Of Volatility And Measure Of VaR

One thing in common of the existing GARCH model based on mixed-frequency samples:when constructing the volatility model,only high-frequency variables are introduced into the volatility equation,and the influence of high-frequency variables on the mean-value equation is not considered.This research not only introduce high-frequency variables into the volatility equation,but also add high-frequency variables to the mean-value equation when constructing a GARCH model based on mixed-frequency samples.The research divides the daily transaction time into two periods and their yield sequence.This research uses two-period yield sequences to construct two mean-value equations of mixed frequencies,and to establish conditional volatility equations for the residuals of each equation.The realized volatility is added as the explanatory variable of conditional volatility in both volatility equations.Then use the sum of two conditional volatility to construct the realized volatility equation and complete the construction of the M-Realized GARCH modelThis research chooses the daily closing price,the first hour closing price and the 5 minutes closing price data of CSI 300 Index as sample of empirical research.The closing price of every 5 minutes is chosen to calculate the high frequency yield of every 5 minutes which can be used to calculate the realized volatility.Under the assumption that the disturbance terms obey normal distribution,t distribution,and generalized error distribution(GED)respectively,the rolling time window is used to perform one-step out-of-sample prediction of the volatility.And the corresponding VaR is calculated from the above fluctuation prediction value.The loss functions(MSE,MAE,MSPE,MAPE,R2LOG,and six robust loss fimctions)and SPA tests are used to analyze the difference in volatility prediction accuracy for different volatility models under different assumptions of disturbance item distribution.Conducting Kupiec test and Dynamic Quantile test to study the effect of VaR prediction from different volatility models based on the assumption of different perturbation terms distribution.Empirical research results based on the CSI 300 Indices show that there are significant differences in the parameter estimation results of different volatility models.For the same volatility model with different assumptions of distribution of disturbance items,there are also some differences in parameter estimation results.According to the parameter estimation results of the M-Realized GARCH model,there is a positive feedback effect on the opening trading of today's open market trading during the period after the last trading day,and there is an intraday momentum effect on the rate of return.The relative loss function shows that the M-Realized GARCH model has higher prediction accuracy.The SPA test indicates that the M-Realized GARCH model under the assumption that the disturbance term obeys the t distribution is the highest accuracy of volatility prediction Kupiec test and Dynamic Quantile test show that the actual failure rate is consistent with the theoretical failure rate of VaR based on the M-Realized GARCH model,and there is no correlation between the failure occurrence.5000-time-simulation tests indicate that the in-sample forecasting accuracy of the M-Realized GARCH model for volatility is significantly higher than that of the GARCH model and the Realized GARCH model.For the M-Realized GARCH model,the volatility prediction accuracy is higher under the assumption that the disturbance term obeys the normal distribution than the t distribution and the generalized error distribution(GED).