序列相关下多变点检测：Wild对比最大化与gappy Schwarz算法
Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm
AI总结：
本文提出WCM.gSa方法，结合Wild对比最大化与gappy Schwarz算法，用于在自相关线性时间序列中一致地检测均值多变点的数量与位置，并通过模拟和伦敦空气质量数据验证其有效性。
摘要：
我们提出一种方法，用于检测其他方面平稳、自相关、线性时间序列均值中的多个变点。该方法结合了基于Wild对比最大化原理的解路径生成，以及一种基于信息准则的模型选择策略，称为gappy Schwarz算法。前者非常适合将均值偏移与由序列相关性引起的波动区分开来，而后者同时估计依赖结构和变点数量，无需执行估计噪声水平的困难任务，例如通过长期方差来量化噪声水平。我们对其理论性质进行了模块化研究，并表明这种名为WCM.gSa的组合方法在估计变点总数和位置方面具有一致性。通过广泛的模拟研究展示了WCM.gSa的良好性能，并进一步通过将该方法应用于伦敦空气质量数据来说明其实用性。
英文摘要：
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.
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