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

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。

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

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 time-varing, clustering and nonlinear features of volatility,and describing regime switching process of low-high volatility of Shanghai Stock Exchange.