  We study the problem of detecting and locating change points in
high-dimensional Vector Autoregressive (VAR) models, whose transition matrices
exhibit low rank plus sparse structure. We first address the problem of
detecting a single change point using an exhaustive search algorithm and
establish a finite sample error bound for its accuracy. Next, we extend the
results to the case of multiple change points that can grow as a function of
the sample size. Their detection is based on a two-step algorithm, wherein the
first step, an exhaustive search for a candidate change point is employed for
overlapping windows, and subsequently, a backward elimination procedure is used
to screen out redundant candidates. The two-step strategy yields consistent
estimates of the number and the locations of the change points. To reduce
computation cost, we also investigate conditions under which a surrogate VAR
model with a weakly sparse transition matrix can accurately estimate the change
points and their locations for data generated by the original model. This work
also addresses and resolves a number of novel technical challenges posed by the
nature of the VAR models under consideration. The effectiveness of the proposed
algorithms and methodology is illustrated on both synthetic and two real data
sets.
