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We consider the problem of multiple change-point estimation in the mean of aGaussian AR(1) process. Taking into account the dependence structure does notallow us to use the dynamic programming algorithm, which is the only algorithmgiving the optimal solution in the independent case. We propose a robustestimator of the autocorrelation parameter, which is consistent and satisfies acentral limit theorem. Then, we propose to follow the classical inferenceapproach, by plugging this estimator in the criteria used for change-pointsestimation. We show that the asymptotic properties of these estimators are thesame as those of the classical estimators in the independent framework. Thesame plug-in approach is then used to approximate the modified BIC and choosethe number of segments. This method is implemented in the R package AR1seg andis available from the Comprehensive R Archive Network (CRAN). This package isused in the simulation section in which we show that for finite sample sizestaking into account the dependence structure improves the statisticalperformance of the change-point estimators and of the selection criterion.

A robust approach for estimating change-points in the mean of an AR(1) process