考虑微观结构噪声与测量误差的波动率预测

Volatility Forecasting in the Presence of Microstructure Noise and Measurement Error

以测量误差的分布理论为基础,本文将微观结构噪声的影响引入到测量误差的方差中,构建了包含微观结构噪声影响的HARQ-N模型。使用蒙特卡洛模拟与中国股市的高频数据对HAR、HARQ、HARQ-N模型与HAR-RV-N-CJ模型的估计和预测进行了比较,研究发现,HARQ模型和HARQ-N模型的测量误差修正项对波动率的影响系数统计显著为负,HARQ-N模型的测量误差项影响系数远大于HARQ模型,更大程度地减弱当期微观结构噪声和测量误差的影响。并且,考虑微观结构噪声和测量误差的HARQ-N模型样本内和样本外预测效果在统计上显著优于HAR模型、HARQ模型与HAR-RV-N-CJ模型。

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.