  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.
