A robust approach for estimating change-points in the mean of an autoregressive process

We consider the problem of multiple change-point estimation in the mean of an autoregressive process.  Taking into account the (homogeneous) 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 autoregression
parameters, 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. We show with simulations that for finite sample sizes taking into account the dependence structure improves the statistical performance of the change-point estimators and of the selection criterion. Then we discuss the problem of joint model selection of the number of change-points and the order of the autoregression.