幂变换门限GARCH模型变点问题的贝叶斯分析

Bayesian analysis of power-transformed and threshold GARCH model with change-point

用贝叶斯方法对幂变换门限GARCH (PTTGARCH)模型变点问题进行统计分析.构造了变点模型参数的满条件分布并且采用MCMC的Griddy-Gibbs抽样算法对参数进行了估计.分别就不同的变点位置、模型不存在变点以及模型接近非平稳的情况进行数值模拟.结果表明:变点处于序列中间位置时,估计效果较好,当变点位置越靠近序列两端时,所得估计的误差越大;当模型不存在变点时,所设变点位置τ后验分布的峰度接近均匀分布的峰度;当模型存在变点时,τ后验分布的峰度大于2,且模型越平稳,τ的后验分布的峰度越大,因此可以通过判断τ的后验分布的峰度来判断模型是否存在变点.最后以GARCH模型对上证指数日收益率进行分析,得到变点发生时刻的概率分布,该结果与市场的变化背景符合.

The purpose of this paper is to analyze the change-point problem for the power-transformed and threshold GARCH(PTTGARCH)model with the Bayesian method.Meanwhile,we construct the full conditional distribution of parameters in the model and estimate the parameters with the Griddy-Gibbs sampling algorithm.The numerical simulation is carried out under three different conditions:the change-point in different positions,the model without change-point,and the nearly non-stationary model.The result shows that,firstly,when the change-point is in the middle position of the sequence,the estimation performs well.In other words,the change-point is closer to both ends of the sequence,the error of the estimation is larger.Secondly,when there is no change-point in the model,the kurtosis of the posterior distribution of the change-pointτis close to that of uniform distribution.Thirdly,when the model which is stationary has a change-point,the kurtosis ofτ's posterior distribution is greater than 2;the smoother the model is,the greater the kurtosis ofτ's posterior distribution is.Therefore,it is possible to examine the existence of the change-point in a stationary model through the kurtosis of theτ's posterior distribution.Finally,this paper applies the GARCH model to analyze the Shanghai Composite,and obtains the probability distribution of the change-point.This result is consistent with the changes in the stock market.