Parameter Estimation Of GARCH Model Based On High Frequency Data

As the popularity of electronic trading systems, intraday high-frequency data in addition to daily close-to-close data can be obtained conveniently. In general, there may be more information included in such data set. Visser (2011) proposed a novel scaling model which embeds the intraday return processes into GARCH framework for daily returns. So it can be used to improve the parameters’estimation of GARCH model by constructing proper volatility proxies. However, high-frequency data always bring noises and outliers which may lead to big bias of the estimations. Therefore, when intraday high-frequency data are used for modeling, one should take microstructure noises into account. We should use estimators which are less restricted and more robust.Based on the above considerations, this paper proposes quasi-maximum exponen-tial likelihood estimators (QMELE) for the GARCH volatility proxy model. Asymp-totic properties of QMLE are studied. Compared to QMLE, The asymptotic normality of QMELE just requires finite second moment of the innovations. A simulation study is carried out to assess the performance of QMELE and the results show QMELE is more accurate and robust than QMLE.Moreover, we consider a class of robust M-estimates for the GJR volatility proxy model. Asymptotic results are established for the robust M-estimates without the fi-nite fourth moment of the innovations which is needed for QMLE. Meanwhile, we can gain efficiency by constructing proper loss functions. We also conduct Monte Carlo simulations to compare the finite sample performances of these robust M-estimates. The results show that the robust M-estimates perform better than others when realized volatility is used as a proxy regardless of with or without outliers contamination. Even for the case of25%contaminated samples, they still have good performance and high efficiency.Finally, this paper discribes how to use the volatility proxy model to predict value at risk (VaR). An empirical study for predicting VaR of CSI300Index is conducted to compare performaces of different models and estimators. The empirical results prove the validity and accuracy of the various estimates proposed by this paper, and confirm the practicality of the volatility proxy model.In summary, the proposed estimations for volatility proxy model, as well as the VaR method have good statistical properties and practicality. In practical applications, they have great significance.