T分布下AR-GARCH模型的贝叶斯估计

Bayesian Estimation of AR-GARCH Model with T Distribution

针对传统估计方法的不足,结合后验分布理论,构造合理的先验分布,应用贝叶斯原理,推断出T分布下AR-GARCH模型的后验密度函数,并应用马尔科夫蒙特卡罗方法(MCMC)对参数贝叶斯估计,且进行实证研究.结果表明:无论方差方程系数参数先验分布服从什么分布(均匀分布﹑正态分布﹑伽玛分布),其后验分布总是伽玛分布,且先验分布与后验分布共轭时,贝叶斯估计与极大似然估计最接近,但方差信息准则最大;先验分布为均匀分布时,方差信息准则最小.正态分布下AR-GARCH模型的结论与T分布下的结论一致.

This paper presents reasonable prior distribution to improve the traditional estimation method by applying posterior distribution theory. Then, Bayesian principles are used to infer the posteriori density function for AR-GARCH Model with T distribution, and Markov Monte Carlo methods （MCMC） are also used for Bayesian parameter estimation. Empirical research is carried out, indicating the following results. Firstly, the posterior distribution is always gatmna distribution, no matter the prior distribution of variance equation coefficients obeys uniform distribution or normal distribution or even gamma distribution. Secondly, when the prior distribution and the posterior distribution are conjugated, the Bayesian estimation and ~naximum likelihood estimation is closest among all kinds of parameter estimations, but with the largest deviance information criterion. Thirdly, the minimum deviance information criterion can be found when the prior distribution is uniform. Finally, in the case of normal distribution, AR-GARCH model and T distribution share the same results.