动态混合HGARCH模型的估计和预测  

Estimation and forecasting of mixture HGARCH model

作　　者：李木易 方颖[1,2,3] LI Mu-yi;FANG Ying(MOE Key Laboratory of Econometrics(Xiamen University),Xiamen 361005,China;The Wang Yanan Institute for Studies in Economics(WISE),Xiamen University and Department of Statistics,School of Economics,Xiamen University,Xiamen 361005,China;Fujian Key Laboratory of Statistical Science(Xiamen University),Xiamen 361005,China)

机构地区：[1]教育部计量经济学重点实验室(厦门大学),厦门361005 [2]厦门大学王亚南经济研究院与经济学院,厦门361005 [3]福建省统计科学重点实验室(厦门大学),厦门361005

出　　处：《管理科学学报》2020年第5期1-12,共12页Journal of Management Sciences in China

基　　金：国家自然科学基金重点资助项目(71631004);国家自然科学基金资助项目(71671150,11771361);国家杰出青年科学基金资助项目(71625001);国家基础科学中心资助项目(71988101)。

摘　　要：在GARCH模型框架下,提出过新的双曲GARCH形式(记为HGARCH),不仅与HY-GARCH模型一样可以同时刻画波动的强烈振幅和长记忆衰减两个性质,并且较之HY-GARCH模型,有更简单的条件方差非负约束条件.然而,当时间序列较长时,用单一参数结构不能充分捕捉可能发生的结构变化.为此,提出新的动态混合HGARCH模型(DM-HGARCH),使之可以同时拥有协方差平稳、长记忆和结构变化3个特性.讨论了新模型的弱平稳解存在条件,利用EM算法进行参数估计,并且用蒙特卡罗模拟给出估计在有限样本下的表现.最后将该模型分别用于1995年~2014年中国上证指数和美国标普500指数的日波动率建模.结果表明,在给定样本期间内,动态混合HGARCH模型(DM-HGARCH)对标普500指数有更好的样本内拟合和样本外预测表现.In the framework of GARCH models,Li et al.(2015)proposed a new hyperbolic GARCH model(denoted by HGARCH),which can parameterize both long memory decay and dramatic amplitude of volatilities as the HY-GARCH model(Davidson,2004).What’s more,the non-negative restrictions on the parameters in the HGARCH model are more tractable than those counterparts in HY-GARCH models.However,it is well known that when the time series covers a long time span,a constant structure is usually inadequate to capture possible structure changes.To address this issue,this paper constructs a new dynamic mixture hyperbolic GARCH(denoted by DM-HGARCH)model.The DM-HGARCH model accommodates covariance stationarity,long memory and structural changes in volatilities simultaneously.Conditions for the existence of weak stationary solutions are investigated and the EM algorithm is employed for parameter estimation.MonteCarlo simulations are conducted to evaluate the finite-sample performance.Finally,the new model is applied to the daily log returns of Shanghai stock exchange(SSE)index in China and S&P 500 index in USA respectively.The empirical study illustrates that in the given sample period,the DM-HGARCH performs better on the latter index than the former one in terms of both in-sample fitting and out-of-sample forecasting.

关 键 词：动态混合 长记忆波动率 双曲GARCH模型 EM算法 

分 类 号：O212[理学—概率论与数理统计]