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.

本文针对自回归时间序列模型中的附加异常值群检测问题，提出了一种改进方法。该方法借助吉布斯采样（Gibbs sampling）对现有检测方案进行优化。本文结合贝叶斯方法与卡尔曼平滑器（Kalman smoother）构建了多组异常值群候选模型，并从中选取贝叶斯信息准则（Bayesian Information Criterion, BIC）值最小的最优模型。本文提出，这种贝叶斯-卡尔曼联合方法（CBK）能够有效削弱附加异常值群检测过程中的掩盖效应与淹没效应。最后，本文通过模拟数据与实际观测数据集验证了该方法的正确性与有效性。