  Autoregressive models capture stochastic processes in which past realizations
determine the generative distribution of new data; they arise naturally in a
variety of industrial, biomedical, and financial settings. A key challenge when
working with such data is to determine when the underlying generative model has
changed, as this can offer insights into distinct operating regimes of the
underlying system. This paper describes a novel dynamic programming approach to
localizing changes in high-dimensional autoregressive processes and associated
error rates that improve upon the prior state of the art. When the model
parameters are piecewise constant over time and the corresponding process is
piecewise stable, the proposed dynamic programming algorithm consistently
localizes change points even as the dimensionality, the sparsity of the
coefficient matrices, the temporal spacing between two consecutive change
points, and the magnitude of the difference of two consecutive coefficient
matrices are allowed to vary with the sample size. Furthermore, the accuracy of
initial, coarse change point localization estimates can be boosted via a
computationally-efficient refinement algorithm that provably improves the
localization error rate. Finally, a comprehensive simulation experiments and a
real data analysis are provided to show the numerical superiority of our
proposed methods.
