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:本文提出了一种方法,用于检测在静止自相关线性时间序列的平均值中的多个变点。该方法结合了基于野外对比度最大化原则的解路径生成和一种基于信息准则的模型选择策略,称为间隔式Schwarz算法。前者非常适合将平均值的变化与由于串行相关性而导致的波动分离开来,而后者同时估计了依赖结构和变点数量,而无需像长期方差那样估计噪声水平。我们对它们的理论属性进行了模块化调查,并表明WCM.gSa(所称的组合方法)在估计变点的数量和位置方面都达到了一致性。通过广泛的模拟研究,WCM.gSa的良好表现得到了证明,并通过将该方法应用于伦敦空气质量数据来进一步说明其有用性。