A robust approach for estimating change-points in the mean of an AR(p) process
We consider the problem of change-points estimation in the mean of an AR(p) process. Taking into account the dependence structure does not allow us to use the 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 two-step method, based on the preliminary robust (to the change-points) estimation of the autoregression parameters. Then, we propose to follow the classical approach, by plugging this estimator in the criterion used for change-point estimation, which is equivalent to decorrelate the series using the estimated autoregression parameters. We show that the asymptotic properties of these change-point location and mean 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, and to derive a heuristic BIC criterion to select both the number of changes and the order of the autoregression. 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.