A robust approach to multiple change-point estimation in an AR(1) process

We consider the problem of multiple change-point estimation in the mean of a Gaussian AR(1) process. Taking into account the dependence structure does not allow us to use the inference approach of the independent case. Especially, the dynamic programming algorithm giving the optimal solution in the independent case cannot be used anymore. We propose a robust estimator of the autocorrelation parameter, which is consistent and satisfies a central limit theorem. Then, we propose to follow the classical inference approach, by plugging this estimator in the criteria used for change-points estimation. We show that the asymptotic properties of these estimators are the same as those of the classical estimators in the independent framework. The same plug-in approach is then used to approximate the modified BIC and choose the number of segments. Finally, we show, in the simulation section, that for finite sample size taking into account the dependence structure improves the statistical performance of the change-point estimators and of the selection criterion.