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本文将Hansen等(2012)的Realized GARCH模型扩展为包含日内收益率、日收益率以及已实现波动率的混频已实现GARCH模型(M-Realized GARCH模型)。该模型将日内交易分为前后两段,引入了混频均值方程,并对混频均值方程的残差分别建立条件波动率方程和已实现日波动率方程。本文采用2013—2016年沪深300指数混频数据,分别在扰动项服从正态分布、t分布和广义误差分布的假设下,采用损失函数、SPA检验、kupiec检验和动态分位数检验法,对GARCH、Realized GARCH和MRealized GARCH模型的波动率预测和VaR度量效果进行对比研究,得出M-Realized GARCH模型能提高预测精度,且VaR实际失败率与理论失败率一致,失败发生之间不相关。最后,本文利用Block bootstrap方法抽样得到混频数据,模拟证明了M-Realized GARCH模型比Realized GARCH模型具有更高的预测精度。
Abstract：This paper extends Hansen et al.( 2012) 's Realized GARCH model to a mixed frequency Realized GARCH model( M-Realized GARCH model),including the data of intraday return,daily return and realized volatility. In our new model,we divide each trading day into two periods,and add mix frequency mean equations. We both build the conditional volatility equation of the residuals in mean equations and realized volatility equation. Mix frequency data of CSI 300 index 's during 2013—2016 are analyzed in this paper.Different distributions including normal distribution, t distribution and generalized error distribution are discussed too. The results of Loss function,SPA Test,kupiec Test and Dynamic Quantile Test show that the volatility predict power measure of VaR of M-Realized GARCH model are better than the GARCH,Realized GARCH. Moreover,actual failure rate of VaR is consistent with the theoretical failure rate,and there is no correlation between the two failures occurred. In the end,we use Block bootstrap method to sample mix frequency data,and further prove that the M-Realized GARCH model has higher prediction accuracy than the Realized GARCH model.
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(1)若无特殊说明,本文的扰动项均考虑分别服从正态分布、t分布和广义误差分布(GED)。
(1)准确地说,ht应该是波动率的平方,为了和已实现波动率RV称呼对应,本文均将ht称为波动率。
(1)9个模型记为GARCH_n、GARCH_t、GARCH_GED、Realized GARCH_n、Realized GARCH_t、Realized GARCH_GED、M-Realized GARCH_n、M-Realized GARCH_t、M-Realized GARCH_GED。n、t、GED分别代表正态分布、t分布和GED分布。
(1)限于篇幅的限制,p值的均值未列出。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2018.01.011
中图分类号:F832.51;O212
引用信息:
[1]于孝建,王秀花.基于混频已实现GARCH模型的波动预测与VaR度量[J].统计研究,2018,35(01):104-116.DOI:10.19343/j.cnki.11-1302/c.2018.01.011.
2018-01-25
2018-01-25