基于MH算法的贝叶斯分位自回归模型

Bayesian Inference on the Quantile Autoregressive Models with Metropolis-hastings Algorithm

针对时间序列分布特征多样性的问题,不考虑序列本身的分布特征而选择非对称Laplace分布的似然函数对模型进行贝叶斯分位回归分析.利用Metropolis-Hastings算法模拟参数的后验边缘分布,解决了参数估计过程遇到的高维数值积分的问题.仿真分析中,参数的迭代轨迹是收敛的,说明MH抽样有效地模拟了参数的后验边缘分布;并且应用该方法估计出了不同分位数下模型参数的后验均值,标准差,MC误差和95%的置信区间.非对称和局部持续性数据的数值模拟,证实了贝叶斯分位自回归模型可以更全面有效地描述滞后变量对响应变量变化范围和条件分布形状的影响.

To address the problem that the distribution feature of time series could not always be easily described due to its diversity, the likelihood function based on the asymmetric Laplace distribution was employed irrespective of the original distribution of the data. To carry out Bayesian inference on the quantile autoregression, the Metropolis-Hastings algorithm was utilized to simulate the posterior marginal distribution of quantile autoregressive parameters,which resolved the difficulties of the high dimension numerical integral. The simulation result has shown that the MH algorithm is effective in simulating the posterior marginal densities because trace plots are convergent. The posterior mean, standard deviation, MC error and 95 % posterior confidence interval of the quantile autoregressive parameters were estimated, which has comprehensively described how lag variables influence the location, scale and shape of the conditional distribution of the response.