  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.
