We propose a methodology for detecting multiple change points in the mean of an otherwise stationary, autocorrelated, linear time series. It combines solution path generation based on the wild contrast maximisation principle, and an information criterion-based model selection strategy termed gappy Schwarz algorithm. The former is well-suited to separating shifts in the mean from fluctuations due to serial correlations, while the latter simultaneously estimates the dependence structure and the number of change points without performing the difficult task of estimating the level of the noise as quantified e.g.\ by the long-run variance. We provide modular investigation into their theoretical properties and show that the combined methodology, named WCM.gSa, achieves consistency in estimating both the total number and the locations of the change points. The good performance of WCM.gSa is demonstrated via extensive simulation studies, and we further illustrate its usefulness by applying the methodology to London air quality data.

翻译：我们提出一种用于检测序列相依线性时间序列（除均值变化外保持平稳且自相关）中均值多变点的方法论。该方法将基于野值对比最大化原理的路径生成策略与基于信息准则的模型选择算法（称为间隙施瓦茨算法）相结合。前者特别适用于分离均值偏移与序列相关引起的波动，而后者无需执行估计噪声水平（如长期方差所量化）的困难任务，即可同步估计相依结构与变点数量。我们对其理论性质进行了模块化研究，并证明组合方法WCM.gSa在估计变点总数与位置时具有相合性。通过大量模拟研究验证了WCM.gSa的优越性能，并将其应用于伦敦空气质量数据以进一步展示其实用价值。