厚尾随机波动率模型的贝叶斯参数估计及实证研究

Bayesian Estimation of the Thick-Tailed Stochastic Volatility Model--Empirical Study of Shanghai Composite Index

针对现有时间序列模型难以刻画参数渐变性的问题,对厚尾随机波动(SV)模型的参数估计方法进行了推广,采用基于贝叶斯的MCMC方法,选取2013年5月~2016年6月这一经历多轮震荡的上证指数作为实证分析对象,构造了基于Gibbs抽样的MCMC过程进行仿真分析.结果显示,以卡方分布作为厚尾参数的先验分布能够有效地描述数据波动的厚尾特征,并且能得到较高精度的参数估计结果.结果表明,厚尾SV模型能有效反映出我国股市尖峰厚尾和波动长期记忆性的特征.

To solve the problem that the current stochastic volatility model cannot describe the characteristics of parameters＇ time-changing property,this paper extended the parameter estimation methodology of the thick-tailed stochastic volatility model, and chose the Shanghai Composite Index from May. 2013 to June. 2016 as empirical study samples which fluctuated several times. Further- more, this paper established the MCMC procedure based on Gibbs sampling method to simulate the model. The result indicates that tak- ing chi-square distribution as the prior distribution of the thick-tailed parameter can describe thick-tailed property of the data precisely and can get more accurate parameter estimation result. According to the reasons above, this paper argues that SVT model can charac- terize the Chinese stock market＇s volatility and long-term memory properties efficiently.