GJR-CAViaR模型的贝叶斯分位数回归——基于Gibbs抽样的MCMC算法实现

发布时间：2018-01-10 11:21

本文关键词：GJR-CAViaR模型的贝叶斯分位数回归——基于Gibbs抽样的MCMC算法实现　出处：《中央财经大学学报》2017年07期 　论文类型：期刊论文

【摘要】：本文将基于Gibbs抽样的MCMC算法引入GJR-CAViaR模型,实现模型的贝叶斯推断。GJR-CAViaR模型是含有递归形式的分位数回归方程,尚未有文献提出如何对其进行贝叶斯分析和MCMC估计。本文首先利用不对称拉普拉斯分布建立GJR-CAViaR模型的似然函数,并通过引入标准指数分布和标准正态分布的混合分布得到不对称拉普拉斯分布的参数解析的条件分布,然后讨论模型的Gibbs抽样过程以及算法实现。对上证综指日收益率数据建立GJR-CAViaR模型,并得到模型参数的贝叶斯估计值。在马尔科夫链收敛的前提下,发现中国证券市场VaR具有自回归性质,且呈现收益对风险的不对称特征。这一特征不会受到样本容量大小及置信水平的影响。
[Abstract]:In this paper, the MCMC algorithm based on Gibbs sampling is introduced into the GJR-CAViaR model. The Bayesian inference. GJR-CAViaR model is a quantile regression equation with recursive form. There is no literature on how to carry out Bayesian analysis and MCMC estimation. Firstly, the likelihood function of GJR-CAViaR model is established by using asymmetric Laplace distribution. By introducing the mixed distribution of standard exponential distribution and standard normal distribution, the analytical conditional distribution of the parameters of the asymmetric Laplace distribution is obtained. Then the paper discusses the Gibbs sampling process and algorithm implementation of the model, and establishes the GJR-CAViaR model for the daily return data of Shanghai Composite Index. The Bayesian estimation of the model parameters is obtained. Under the premise of Markov chain convergence, it is found that VaR in Chinese stock market has autoregressive property. This feature is not affected by sample size and confidence level.
【作者单位】：西北政法大学经济学院;中央财经大学财经研究院;北京财经研究基地;
【分类号】：F224;F832.51
【正文快照】： 法。另一类是借助于贝叶斯原理进行参数估计。直接优化求解属于频率学派的范畴,是传统的经典统计学方法。经典估计方法将参数视为固定常数,然后利用最小二乘或极大似然等方法计算参数的估计值,得到参数的渐近分布和统计性质,并进行假设检验。贝叶斯学派与经典统计法在参数估计

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