As high-frequency data is widely used in forecasting stock volatility, we propose a new family of easy-to-implement models based on realized volatility, which is constructed from the summation of the squared high-frequency intraday returns. In this paper, the estimation error of the realized volatility is assumed to obey the assumption of heteroscedasticity. When modeling the volatility of stock market, we set the autoregressive coefficients of the model according to the change of estimation errors' variances and get HARQ (F) model. In the meantime, we propose HARQ (F)-CJ model and LHARQ (F)-CJ model in combination with the jump behavior and leverage effect of Chinese stock market volatility to improve the fitness and predictive power of the realized volatility model. We suppose, the larger the estimation error's variance of the realized volatility or the continuous component in the current period, the worse its interpretation of the latent volatility in the future,and the smaller the corresponding coefficient is. Through an empirical study on the high-frequency data of the Shanghai Composite Index from December 31st, 2015 to January 2nd, 2001, we find that based on the assumption of heteroscedasticity in the estimation errors, dynamic coefficients can improve the fitness and the predictive power of the realized volatility model. Above all, the dynamic adjustment of daily regression coefficient based on estimation error variance is the key to improve the fitness and predictive power of the model. The LHARQ-CJ model in combination with both the jump behavior and the leverage effect of the Chinese stock market is considered to show the best performance in all related models. Finally, this research has made its contribution in modeling and forecasting Chinese stock volatility with dynamic estimation errors and dynamic autoregressive coefficients.
SONG Ya-qiong, WANG Xin-jun
. Modeling and Forecasting Volatility of Chinese Stock Market Based on Dynamic Estimation Errors[J]. Chinese Journal of Management Science, 2017
, 25(9)
: 19
-27
.
DOI: 10.16381/j.cnki.issn1003-207x.2017.09.003
[1] Andersen T G,Bollerslev T. Deutsche Mark-Dollar Volatility:Intraday activity patterns, macroeconomic announcements and longer run dependencies[J]. Journal of Finance, 1998, 53(1):219-265.
[2] Andersen T G, Bollerslev T, Diebold F X, et al. Modeling and forecasting realized volatility[J]. Econometrica, 2003, 71(2):579-625.
[3] Corsi F. A simple approximate long-memory model of realized volatility[J]. Journal of Financial Econometrics, 2009, 7(2):174-196.
[4] 魏宇. 沪深300股指期货的波动率预测模型研究[J]. 管理科学学报,2010,13(2):66-76.
[5] Andersen T G, Bollerslev T, Diebold F X. Roughing it up:Including jump components in the measurement, modeling, and forecasting of return volatility[J]. Review of Economics and Statistics, 2007, 89(4):701-720.
[6] Bollerslev T, Kretschmer U, Pigorsch C, et al. A discrete-time model for daily S&P500 returns and realized variations:Jumps and leverage effects[J]. Journal of Econometrics, 2009, 150(2):151-166.
[7] Corsi F, Reno R. HAR volatility modeling with heterogeneous leverage and jumps[R].Working Paper, University of Lugano, 2009b.
[8] 陈浪南,杨科. 中国股市高频波动率的特征、预测模型以及预测精度比较[J]. 系统工程理论与实践, 2013,33(2):296-307.
[9] 孙洁. 考虑跳跃和隔夜波动的中国股票市场波动率建模与预测[J]. 中国管理科学,2014, 22(6):114-124.
[10] Asai M, Mcaleer M, Medeiros M C. Modelling and forecasting noisy realized volatility[J]. Computational Statistics and Data Analysis, 2012, 56(1):217-230.
[11] Dobrev D P, Szerszen P J. The information content of high-frequency data for estimating equity return models and forecasting risk[R]. Working Paper, Federal Reserve Board, 2010.
[12] Jacod J, Li Yingying, Mykland P A, et al. Microstructure noise in the continuous case:the preaveraging approach[J]. Stochastic Processes and Their Applications. 2009, 119(7):2249-2276.
[13] Andersen T G, Bollerslev T, Meddahi N. Realized volatility forecasting and market microstructure noise[J]. Journal of Econometrics, 2011, 160(1):220-234.
[14] Bandi F M, Russell J R. Separating microstructure noise from volatility[J]. Journal of Financial Economics, 2006, 79(3):655-692.
[15] 唐勇. 考虑微观结构噪声与跳跃影响的波动建模[J]. 数学的实践与认识,2012, 42(5):25-36.
[16] 马丹,尹优平. 噪声、跳跃与高频价格波动——基于门限预平均实现波动的分析[J]. 金融研究,2012, 382(4):124-139.
[17] Barndor-Nielsen O E, Shephard N. Impact of jumps on returns and realized variances:Econometric analysis of time-deformed levy process[J]. Journal of Econometrics, 2006,131(1):217-252.
