Abstract: Asset prices are often affected by market friction, and thereby microstructure noise is generated. Noises in asset prices make the prices deviate from the equilibrium. In this situation, asset prices are no longer subjected to a continuous semimartingale process so that realized volatility is no longer a consistent estimator of integrated volatility, so noises should be considered in volatility model. Based on the asymptotic distribution theory of measurement error, the impact of microstructure noise is introduced into the variance of measurement error and HARQ-N model which takes microstructure noise into consideration is developed. The estimation and forecasting of HAR, HARQ, HARQ-N and HAR-RV-N-CJ models are compared using Monte Carlo simulation and high frequency data of Chinese stock market. Simulation and empirical results show that coefficients of measurement error adjustment terms in HARQ model and HARQ-N model are negative and significant; When measurement error get larger, short term volatility provide less information for future volatility. Compared with HARQ model, HARQ-N model places greater weight on the measurement error adjustment term and attenuates the impact of microstructure noise and measurement error more; In terms of in-sample and out-of-sample forecast, HARQ-N model is better than other models and the improvement is statistically significant. There is significant long memory property and persistence in volatility of stock market. Long term volatility has significant influence in the forecasting of different terms volatility, though short term volatility influences mid and long terms volatility less than long term volatility.

Key words: realized volatility, measurement error, microstructure noise, HARQ-N model