波动率合格代理变量的必要条件及其非参数检验
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摘要
在较弱的假设下导出合格波动率代理变量的必要条件,并借助重抽样技术构建了检验该必要条件的非参数方法。用其进行中外股指高频数据的实证研究表明:对于中国股指的数据,采用"已实现波动率"作为代理变量违背了上述必要条件而有不适合作为合格代理变量之虞;但欧美股市的数据却未检测出上述问题。最后,根据实证结果对"已实现波动率"进行适当改造,使其成为能避免上述偏差的改进代理变量。
In view of the importance of volatility proxy for model evaluation,we propose a necessary condition to be qualified proxies of volatility.A robust approach is given to check the condition in order to investigate the justification of realized volatilities as proxies of volatility.This approach works through comparing the performance of proxies in each sub-sample and whole sample respectively.Applying the approach to stock index,we found that there are some evidences which strongly suggest that realized volatilities are not qualified proxies of volatility for Shanghai stock market data,while the evidences that realized volatilities fail to meet the necessary condition were not detected for Europe and America stock market data.Finally,based on the empirical results,this paper further propose a simple method to revise those proxies and a revised volatility proxy is given as well.
In view of the importance of volatility proxy for model evaluation,we propose a necessary condition to be qualified proxies of volatility.A robust approach is given to check the condition in order to investigate the justification of realized volatilities as proxies of volatility.This approach works through comparing the performance of proxies in each sub-sample and whole sample respectively.Applying the approach to stock index,we found that there are some evidences which strongly suggest that realized volatilities are not qualified proxies of volatility for Shanghai stock market data,while the evidences that realized volatilities fail to meet the necessary condition were not detected for Europe and America stock market data.Finally,based on the empirical results,this paper further propose a simple method to revise those proxies and a revised volatility proxy is given as well.
引文
[1] Andersen T G,Bollerslev T.Answering the Skeptics:Yes,Standard Volatility Models Do Provide Accurate Forecasts[J].International Economic Review,1998,39(4).
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[3] Patton A J.Volatility Forecast Comparison Using Imperfect Volatility Proxies[J].Journal of Econometrics,2011,160(1).
[4] Hansen P R,Lunde A.A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data[J].Journal of Financial Econometrics,2005,3(4).
[5]魏宇.金融市场的多分形波动率测度模型及其SPA检验[J].管理科学学报,2009,12(5).
[6]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).
[7]杨科,陈浪南.股市波动率的短期预期模型和预期精度评价[J].管理科学学报,2012,15(5).
[8]王天一,黄卓.高频数据波动率建模—基于厚尾分布的Realized GARCH模型[J].数量经济技术经济研究,2012(5).
[9] Bin Zhou.High-Frequency Data and Volatility in Foreign-Exchange Rates[J].Journal of Business&Economic Statistics,1996,14(1).
[10]Barndorff-Nielsen O E,Hansen P R,Lunde A,Shephard N.Designing Realised Kernels to Measure the Ex-post Variation of Equity Prices in the Presence of Noise[J].Econometrica,2008(76).
[11]Andersen T G,Bollerslev T,Diebold F X,et al.The Distribution of Realized Exchange Rate Volatility[J].Jurnal of the American Statistical Association,2001,96(453).
[12]Zhang L,Mykland P A,A6t-Sahalia Y.A Tale of Two Time Scales:Determining Integrated Volatility with Noisy HighFrequency Data[J].Journal of the American Statistical Association,2005,100(472).
[13]Zhang L.Efficient Estimation of Stochastic Volatility Using Noisy Observations:A Multi-Scale Approach[J].Bernoulli,2006,12(6).
[14]Corsi F,RenòR.Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With ContinuousTime Volatility Modeling[J].Journal of Business&Economic Statistics,2012,30(3).
[15]施雅丰.在GARCH模型框架下发现的波动率“周内效应”可信吗?[J].统计与信息论坛,2015(1).
[16]施雅丰,艾春荣.中国股市波动率的广义周内特征及其预测模型[J].系统工程理论与实践,2016,36(8).
(1)当日“已实现波动率”是指只使用交易时间高频数据计算得到的已实现波动率,其理论上是{roc,t}的波动率代理变量;它经比例因子或式(4)调整后记为全日“已实现波动率”,其理论上是{roc,t}的波动率代理变量。
[2] Hansen P R,Lunde A.Consistent Ranking of Volatility Models[J].Journal of Econometrics,2006,131(1-2).
[3] Patton A J.Volatility Forecast Comparison Using Imperfect Volatility Proxies[J].Journal of Econometrics,2011,160(1).
[4] Hansen P R,Lunde A.A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data[J].Journal of Financial Econometrics,2005,3(4).
[5]魏宇.金融市场的多分形波动率测度模型及其SPA检验[J].管理科学学报,2009,12(5).
[6]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).
[7]杨科,陈浪南.股市波动率的短期预期模型和预期精度评价[J].管理科学学报,2012,15(5).
[8]王天一,黄卓.高频数据波动率建模—基于厚尾分布的Realized GARCH模型[J].数量经济技术经济研究,2012(5).
[9] Bin Zhou.High-Frequency Data and Volatility in Foreign-Exchange Rates[J].Journal of Business&Economic Statistics,1996,14(1).
[10]Barndorff-Nielsen O E,Hansen P R,Lunde A,Shephard N.Designing Realised Kernels to Measure the Ex-post Variation of Equity Prices in the Presence of Noise[J].Econometrica,2008(76).
[11]Andersen T G,Bollerslev T,Diebold F X,et al.The Distribution of Realized Exchange Rate Volatility[J].Jurnal of the American Statistical Association,2001,96(453).
[12]Zhang L,Mykland P A,A6t-Sahalia Y.A Tale of Two Time Scales:Determining Integrated Volatility with Noisy HighFrequency Data[J].Journal of the American Statistical Association,2005,100(472).
[13]Zhang L.Efficient Estimation of Stochastic Volatility Using Noisy Observations:A Multi-Scale Approach[J].Bernoulli,2006,12(6).
[14]Corsi F,RenòR.Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With ContinuousTime Volatility Modeling[J].Journal of Business&Economic Statistics,2012,30(3).
[15]施雅丰.在GARCH模型框架下发现的波动率“周内效应”可信吗?[J].统计与信息论坛,2015(1).
[16]施雅丰,艾春荣.中国股市波动率的广义周内特征及其预测模型[J].系统工程理论与实践,2016,36(8).
(1)当日“已实现波动率”是指只使用交易时间高频数据计算得到的已实现波动率,其理论上是{roc,t}的波动率代理变量;它经比例因子或式(4)调整后记为全日“已实现波动率”,其理论上是{roc,t}的波动率代理变量。