Combining Bayesian method and Kalman smoother for detection additive outlier patches in autoregressive time series

This article proposes a development of detecting patches of additive outliers in autoregressive time series models. The procedure improves the existing detection methods via Gibbs sampling. We combine the Bayesian method and the Kalman smoother to present some candidate models of outlier patches and the best model with the minimum Bayesian information criterion (BIC) is selected among them. We propose that this combined Bayesian and Kalman method (CBK) can reduce the masking and swamping effects about detecting patches of additive outliers. The correctness of the method is illustrated by simulated data and then by analyzing a real set of observations.

本文提出了一种针对自回归时间序列模型中加性异常值群的检测方法改进方案。该方法借助吉布斯采样（Gibbs sampling）优化了现有检测流程。我们结合贝叶斯方法与卡尔曼平滑器（Kalman smoother）构建了若干异常值群候选模型，并从中选取贝叶斯信息准则（Bayesian Information Criterion, BIC）取值最小的最优模型。本文提出，这种贝叶斯-卡尔曼联合方法（Combined Bayesian and Kalman method, CBK）可有效降低加性异常值群检测中的掩盖效应与淹没效应。通过模拟数据与真实观测数据集的分析，验证了该方法的正确性。