基于Gibbs抽样的贝叶斯稳健ARMA模型研究

BAYESIAN ANALYSIS OF ROBUST ARMA MODELS USING GIBBS SAMPLING

针对ARMA模型建模过程中模型识别和参数估计易受观测值异常点影响问题,构建了同时考虑加性异常点和更新性异常点的ARMA模型.运用基于Gibbs抽样的Markov Chain Monte Carlo贝叶斯方法,估计稳健ARMA模型参数,同步确定观测值中异常点的位置,辨别异常点类型.并利用我国人口自然增长数据进行仿真分析,研究结果表明:贝叶斯方法能够有效地识别ARMA序列的异常点.

To solve the problem that the model identification and the parameter estimation in the ARMA models easily affected by the outliers in time series data, this paper constructed a robust ARMA model which has both additive and renewal outliers. The parameters in the robust ARMA models were estimated by Gibbs sampling, and the kinds and locations for the outliers were also determinated simultaneously. The methodology was illustrated by applying it to Chinese population natural increasing, and the results show that the Bayesian method can effectively distinguish the outliers in time series data.