Daily LGARCH model estimation using high frequency data

In this paper, we introduce the intraday high frequency data to estimate the daily linear generalized autoregressive conditional heteroscedasticity (LGARCH) model. Based on the volatility proxies constructed from the intraday high frequency data, the quasi maximum likelihood estimation (QMLE) of the daily LGARCH model and its asymptotic distribution are studied under some regular assumptions. One criterion is also given to choose the optimal volatility proxy according to the asymptotic results. Simulation studies show that the QMLE of the parameters performs well. It is also found that introducing the intraday high frequency data can significantly improve the estimation precision. The proposed method is applied to analyze the SSE 50 Index, which consists of the 50 largest and most liquid A-share stocks listed on Shanghai Stock Exchange. Empirical results show the method is of potential application value.