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We propose a methodology for detecting multiple change points in the mean ofan otherwise stationary, autocorrelated, linear time series. It combinessolution path generation based on the wild contrast maximisation principle, andan information criterion-based model selection strategy termed gappy Schwarzalgorithm. The former is well-suited to separating shifts in the mean fromfluctuations due to serial correlations, while the latter simultaneouslyestimates the dependence structure and the number of change points withoutperforming the difficult task of estimating the level of the noise asquantified e.g.\ by the long-run variance. We provide modular investigationinto their theoretical properties and show that the combined methodology, namedWCM.gSa, achieves consistency in estimating both the total number and thelocations of the change points. The good performance of WCM.gSa is demonstratedvia extensive simulation studies, and we further illustrate its usefulness byapplying the methodology to London air quality data.

Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm