Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm
提出一种在自相关线性时间序列中检测均值多变点的方法，结合野对比度最大化与间隙施瓦茨算法，无需估计噪声水平即可一致估计变点数量和位置，并应用于伦敦空气质量数据。
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.