随机波动模型的马尔可夫链—蒙特卡洛模拟方法——在沪市收益率序列上的应用  

MCMC Estimation for Regime Switching Stochastic Volatility Model and Its Application in Shanghai Stock Exchange

作　　者：刘金全[1] 李楠[1] 郑挺国[2] 

机构地区：[1]吉林大学数量经济研究中心,吉林长春130021 [2]厦门大学王亚南经济研究院,福建厦门361005

出　　处：《数理统计与管理》2010年第6期1026-1035,共10页Journal of Applied Statistics and Management

基　　金：吉林大学"211"工程和"985工程"建设项目;教育部人文社会科学重点研究基地重大课题项目(2007JJD790125);教育部人文社会科学研究项目应急项目资助

摘　　要：针对具有Markov区制转移的、波动均值状态相依的随机波动模型,基于贝叶斯分析,我们推导并给出了对区制转移随机波动模型的MCMC估计方法,其中对参数估计采用Gibbs抽样方法,对潜在对数波动和区制的状态变量估计采用"向前滤波、向后抽样"的多步移动方法;利用该模型,对我国上证综指周收益率进行了实证分析,发现对沪市波动性有较好的描述,捕捉了波动的时变性、聚类性和非线性特征,同时刻画了沪市的高低波动状态转换过程。This paper propose a Markov regime switching stochastic volatility model with state. dependent mean of volatility. On the basis of Bayesian analysis, we derive Markov Chain Monte Carlo （MCMC） method to estimate this regime switching stochastic volatility model, including Gibbs sampling method for parameter estimation and multi-step method called ＂forward filtering and backward sampling＂ for state variables of logarithm volatility and regimes. Using this model, we analyze weekly returns of Shanghai Stock Exchange and find that it describe volatility well, including capturing timevaring, clustering and nonlinear features of volatility, and describing regime switching process of low-high volatility of Shanghai Stock Exchange.

关 键 词：区制转移 随机波动模型 GIBBS抽样 MCMC方法 

分 类 号：O212[理学—概率论与数理统计]