具有稳定分布噪声的ARMA模型的贝叶斯分析及应用

Bayesian Inference for ARMA Model with Stable Innovations,and Applications

稳定分布是正态分布的推广,能够描述诸如方差无限、厚尾、有偏等非正态特征.但该类分布由于通常没有显式的密度函数,这给建模、分析带来了困难.本文采用数据扩充法、切片抽样法以及MCMC方法,给出了具有稳定分布噪声的ARMA模型更为简洁、有效的贝叶斯建模方法.通过对两个模型的模拟分析,说明了稳定分布的一些统计性质和文中建模方法的有效性.将模型应用于一个实际数据集,演示了该类模型的建模方法并展示了该类模型的一些优势.

Stable distributions are generalizations of the normal distribution, which can allow for infinite variance, skewness and arbitrarily heavier tails than the normal distribu- tion. In general there exists no closed form for the probability density function of a stable distribution, which increases the complexity of modeling and analyzing. By using data aug- mentation algorithm, slice sampling and MCMC methods, a simple and efficient Bayesian modeling method for autoregressive moving average （ARMA） models with stable innova- tions is proposed. We illustrate the modeling method and some interesting properties of the models by using data simulated from two time series models with stable innovations. The model is applied to a real financial data set and compared with other competing models, and appears to capture features of the data set better than other competing models.