基于Gibbs抽样的贝叶斯随机波动模型分析

Stochastic volatility is a widespread phenomenon in the data of economic and time series and plays an important role in the study about the financial risk management. In this paper, we first explore the statistical structure of the stochastic volatility model and inference its likelihood function’s concrete form, by which we construct its parameters’ conjugate priors. Then, in terms of the Bayesian theorem, we deduct their conditional posterior distributions. In order to obtain the parameters’ Bayesian estimation value and their intervals, we design an Markov chain Monte Carlo algorithm procedure with Gibbs sampler. Finally, using the Shanghai stock’s comprehensive index and the Shenzhen stock’s composition index, we give an empirical example to illustrate how to use the method surveyed. The results show that the Bayesian method is a valid tool for studying financial time sequence.