Fractional Integration Realized HAR GARCH Model Based On High Frequency Data

Long memory model has been more and more concerned since Hurst (1951) proposed the feature of long memory. Long Memory implies to long-term correlation, that is, the current state will continue to affect the future, which is not negligible for financial risk management. The research of the long memory model is more and more in-depth development, due to the availability of high-frequency data is easier. Since the Realized GARCH model has been proposed by Hansen et al. (2012), it has become one of the main research direction of high-frequency time series.Based on Realized GARCH, FIGARCH, and Realized HAR GARCH models, combining Long Memory Parameter with conditional variance, we propose Fractional Integration Realized HAR GARCH model. Using high-frequency data of 5 minutes about the shanghai index, we compare the market volatility of the fitting effect and prediction ability with Fractional Integration Realized HAR GARCH, FIR-GARCH, Realized HAR GARCH, and Realized GARCH model respectively. From the empirical results, we obtain that the Fractional Integrated Realized HAR GARCH model can better capture the long-term correlation in volatility through the comparison of theory and sample autocorrelation function, and the overall forecasting ability and fitting effect of the model outperforms the present other models. From the results of Monte Carlo simulation, and on the condition that the residual distribution with normal distribution, t distribution, and chi-square distribution, the Fractional Integrated Realized HAR GARCH model outperforms the others.