基于MCMC算法的贝叶斯变结构分位自回归模型研究  

Bayesian Inference on Structure Change in Quantile Autoregressive Models Based on MCMC

作　　者：曾惠芳[1] 熊培银[2] 刘友金[1] 

机构地区：[1]湖南科技大学商学院,湖南湘潭411201 [2]中南大学信息科学与工程学院,湖南长沙410083

出　　处：《数理统计与管理》2016年第2期253-264,共12页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(41301421);国家自然科学基金项目(41271139)

摘　　要：为了更全面细致的刻画时间序列变结构性的特征及其相依性,提出了一类马尔可夫变结构分位自回归模型。利用非对称Laplace分布构建了模型的似然函数,证明了当回归系数的先验分布选择为扩散先验分布时,参数的各阶后验矩都是存在的,并给出了能确定变点位置和性质的隐含变量的后验完全条件分布。仿真分析结果发现马尔可夫变结构分位自回归模型可以全面有效地实现对时间序列数据变结构性的刻画。并应用贝叶斯Markov分位自回归方法分析了中国证券市场的变结构性,结果发现中国证券市场在不同阶段尾部表现出不同的相依性。This paper is concerned with mixture conditional distribution in which a latent discrete state variable that indicates the regime from which a particular observation has been drawn.This state variable is specified to evolve according to a discrete-time discrete-state Markov process,whose transition probabilities can be constrained so that the state variable can either stay at the current value or jump to next higher value.A new full Bayesian approach based on the method of Gibbs sampling is developed by data augmentation,which is achieved by introducing a mixture representation of asymmetric Laplace distribution.The state variables,one for each observation,can be simulated from their joint distribution given the data and the remaining parameters.This result serves to accelerate the convergence of the Gibbs sample.The simulation shows that the method performs very well in quantile regime switching models.The methodology is then applied to analyzing China stock market and provides some interesting results.

关 键 词：分位回归 变结构 贝叶斯方法 MARKOV链 MCMC算法 

分 类 号：F222.3[经济管理—国民经济] O212[理学—概率论与数理统计]