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：我们提出一种方法,用其他固定、自动相关、线性时间序列的平均值来检测多个变化点,它根据野生对比最大化原则,将解决方案路径生成与基于信息标准的模式选择战略(称为偏差Schwarz算法)相结合,前者非常适合将平均值与因序列关联而产生的波动的转移区分开来,而后者则同时估计依赖结构和变化点数目,而不履行按例如长期差异等量化的噪音水平估算的困难任务。我们提供了对其理论特性的模块化调查,并表明称为WCM.gSa的综合方法在估计变化点总数和位置方面实现了一致性。WCM.gsa的良好表现通过广泛的模拟研究得到证明,我们通过对伦敦空气质量数据应用该方法进一步说明其有用性。