已实现波动GAS-HEAVY模型及其实证研究
|
摘要
引入日内高频数据计算的已实现波动,能够提高波动模型预测能力。本文将日收益和已实现波动联合建模,提出一种新的波动模型。选取尺度调整t分布和F分布作为日收益和已实现波动的分布,更为充分和灵活地捕捉厚尾性,采用得分驱动方法设定波动模型更新项,得出广义自回归得分(GAS)波动模型,提高对实际模型的逼近效率。本文对模型遍历性和平稳性进行证明,并与同类模型进行比较。蒙特卡罗模拟实验显示,在数据生成过程误设的情况下本文提出的GAS-HEAVY模型比同类模型具有更好的数据拟合效果。基于沪综指、深成指和沪深300指数2013.1至2017.4日内1分钟高频数据实证分析表明,不同损失函数的SPA检验下GAS-HEAVY模型的波动预测能力显著强于其它同类模型。本文给出的GAS-HEAVY模型为有关理论研究和市场应用提供了新的波动计量工具。
A new volatility model named GAS-HEAVY is introduced to model returns and realized measures of volatility jointly.The key features are fat-tailed distributions for returns and realized volatilities and autoregressive score-driven(GAS)model for dynamics of the latent volatility.By assuming a rescaled t distribution for daily returns and a rescaled Fdistributionfor realized volatility measures,the score dynamics for the latent volatility are robust to outliers and incidental large observations.Parameter restrictions are formulated to prove ergodicity and stationarity.Our simulation study shows that the new model fit data better than other alternatives.An empirical application of our model is provided to daily returns and 1-minute intraday high-frequency prices of Shanghai Composite Index,Shenzhen Component Index and CSI300 Index.The empirical evidences justify the superior volatility predictive ability of the new model in our paper.
A new volatility model named GAS-HEAVY is introduced to model returns and realized measures of volatility jointly.The key features are fat-tailed distributions for returns and realized volatilities and autoregressive score-driven(GAS)model for dynamics of the latent volatility.By assuming a rescaled t distribution for daily returns and a rescaled Fdistributionfor realized volatility measures,the score dynamics for the latent volatility are robust to outliers and incidental large observations.Parameter restrictions are formulated to prove ergodicity and stationarity.Our simulation study shows that the new model fit data better than other alternatives.An empirical application of our model is provided to daily returns and 1-minute intraday high-frequency prices of Shanghai Composite Index,Shenzhen Component Index and CSI300 Index.The empirical evidences justify the superior volatility predictive ability of the new model in our paper.
引文
[1]Andersen T G,Bollerslev T,Diebold F X,et al.The distribution of realized exchange rate volatility[J].Journal of the American Statistical Association,2001,96(453):42-55.
[2]Hansen P R,Lunde A.Realized variance and market microstructure noise[J].Journal of Business and Economic Statistics,2006,24(2):127-161.
[3]Hansen P R,Huang Zhuo,Shek H H.Realized GARCH:A joint model of returns and realized measures of volatility[J].Journal of Applied Econometrics,2012,27(6):877-906.
[4]Hansen P R,Huang Zhuo.Exponential GARCH modeling with realized measures of volatility[J].Journal of Business and Economic Statistics,2016,34(2):269-287.
[5]Shephard N,Sheppard K.Realising the future:Forecasting with high frequency based volatility(HEAVY)models[J].Journal of Applied Econometrics,2010,25(2):197-231.
[6]Opschoor A,Janus P,Lucas A,et al.New HEAVYmodels for fat-tailed realized covariance and returns[J].Journal of Business and Economic Statistics,2018,36(4):643-657.
[7]Creal D,Koopman S,Lucas A.Generalized autoregressive score models with applications[J].Journal of Applied Econometrics,2013,28(5):777-795.
[8]Blasques F,Koopman S,Lucas A.Information-theoretic optimality of observation-driven time series models for continuous responses[J].Biometrika,2015,102(2):325-343.
[9]Koopman S,Lucas A,Scharth M.Predicting time-varying parameters with parameters-driven and observation-driven models[J].The Review of Economics and Statistics,2016,98(1):97-110.
[10]杨科,陈浪南.上证综指的已实现波动率预测模型[J].数理统计与管理,2013,32(1):165-179.
[11]杨科,田凤平,林洪.跳跃的预测、股市波动率的预测以及预测精度评价[J].中国管理科学,2013,21(3):50-60.
[12]瞿慧,李浩,程昕.HAR族模型与GARCH族模型对不同期限波动率的比较-基于沪深300指数高频价格的实证分析[J].系统工程,2015,33(3):32-37.
[13]吴恒煜,夏泽安,聂富强.引入跳跃和结构转换的中国股市已实现波动率研究:基于拓展的HAR-RV模型[J].数理统计与管理,2015,34(6):1111-1128.
[14]吴鑫育,李心丹,马超群.门限已实现随机波动率模型及其实证研究[J].中国管理科学,2017,25(3):11-19.
[15]Hansen P R.A test for superior predictive ability[J].Journal of Business and Economic Statistics,2005,23(4):365-380.
[16]Koopman S,Scharth M.The analysis of stochastic volatility in the presence of daily realized measures[J].Journal of Financial Econometrics,2012,11(1):76-115.
[17]Hamilton J.Time series analysis[M].Princeton:Princeton University Press,1994.
[18]Barndorff-Nielsen O E,Hansen P R,Lunde A,et al.Realized kernels in practice:Trades and quotes[J].The Econometrics Journal,2009,12(3):C1-C32.
[2]Hansen P R,Lunde A.Realized variance and market microstructure noise[J].Journal of Business and Economic Statistics,2006,24(2):127-161.
[3]Hansen P R,Huang Zhuo,Shek H H.Realized GARCH:A joint model of returns and realized measures of volatility[J].Journal of Applied Econometrics,2012,27(6):877-906.
[4]Hansen P R,Huang Zhuo.Exponential GARCH modeling with realized measures of volatility[J].Journal of Business and Economic Statistics,2016,34(2):269-287.
[5]Shephard N,Sheppard K.Realising the future:Forecasting with high frequency based volatility(HEAVY)models[J].Journal of Applied Econometrics,2010,25(2):197-231.
[6]Opschoor A,Janus P,Lucas A,et al.New HEAVYmodels for fat-tailed realized covariance and returns[J].Journal of Business and Economic Statistics,2018,36(4):643-657.
[7]Creal D,Koopman S,Lucas A.Generalized autoregressive score models with applications[J].Journal of Applied Econometrics,2013,28(5):777-795.
[8]Blasques F,Koopman S,Lucas A.Information-theoretic optimality of observation-driven time series models for continuous responses[J].Biometrika,2015,102(2):325-343.
[9]Koopman S,Lucas A,Scharth M.Predicting time-varying parameters with parameters-driven and observation-driven models[J].The Review of Economics and Statistics,2016,98(1):97-110.
[10]杨科,陈浪南.上证综指的已实现波动率预测模型[J].数理统计与管理,2013,32(1):165-179.
[11]杨科,田凤平,林洪.跳跃的预测、股市波动率的预测以及预测精度评价[J].中国管理科学,2013,21(3):50-60.
[12]瞿慧,李浩,程昕.HAR族模型与GARCH族模型对不同期限波动率的比较-基于沪深300指数高频价格的实证分析[J].系统工程,2015,33(3):32-37.
[13]吴恒煜,夏泽安,聂富强.引入跳跃和结构转换的中国股市已实现波动率研究:基于拓展的HAR-RV模型[J].数理统计与管理,2015,34(6):1111-1128.
[14]吴鑫育,李心丹,马超群.门限已实现随机波动率模型及其实证研究[J].中国管理科学,2017,25(3):11-19.
[15]Hansen P R.A test for superior predictive ability[J].Journal of Business and Economic Statistics,2005,23(4):365-380.
[16]Koopman S,Scharth M.The analysis of stochastic volatility in the presence of daily realized measures[J].Journal of Financial Econometrics,2012,11(1):76-115.
[17]Hamilton J.Time series analysis[M].Princeton:Princeton University Press,1994.
[18]Barndorff-Nielsen O E,Hansen P R,Lunde A,et al.Realized kernels in practice:Trades and quotes[J].The Econometrics Journal,2009,12(3):C1-C32.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |