基于MCMC的贝叶斯长记忆随机波动模型研究

Markov Chain Monte Carlo Methods for Bayesian Long Memory Stochastic Volatility Models

针对贝叶斯长记忆随机波动模型的单步Gibbs抽样算法效率低下的问题,通过对模型在状态空间框架下的近似表示,将向前滤波向后抽样算法引入对波动变量的估计过程中,同时在贝叶斯框架下分析了模型参数的满条件后验分布,设计出Gibbs联合抽样算法.更进一步,在对模型进行参数估计的基础上,提出波动变量的向前多步预报分布的估计方法.模拟实验结果表明:联合Gibbs抽样算法能够在保证估计精度的基础上得到优于单步Gibbs抽样方法的抽样效率,对预报分布的特征分析可用于对金融时间序列的风险控制.

This paper was concerned with simulation-based inference in generalized models of stochastic volatility with long memory. A more efficient Markov Chain Monte Carlo sampling method was exploited to the analysis of the model, compared with the single step Gibbs sampling method. Based on the truncated likelihood method, in which the long memory stochastic volatility model was expressed as a linear state space model, we utilized the forward filtering backward sampling method to sample all the unobserved volatilities simultaneously. A simulation method for Bayesian prediction analysis of the volatilities was also developed. The simulation study has given the results of estimated parameters and evaluated the performance of our method. Moreover, the prediction analysis of the volatility can be used to control the risk of financial series.