  Vector autoregressive (VAR) models are widely used in multivariate time
series analysis for describing the short-time dynamics of the data. The
reduced-rank VAR models are of particular interest when dealing with
high-dimensional and highly correlated time series. Many results for these
models are based on the stationarity assumption that does not hold in several
applications when the data exhibits structural breaks. We consider a low-rank
piecewise stationary VAR model with possible changes in the transition matrix
of the observed process. We develop a new test of presence of a change-point in
the transition matrix and show its minimax optimality with respect to the
dimension and the sample size. Our two-step change-point detection strategy is
based on the construction of estimators for the transition matrices and using
them in a penalized version of the likelihood ratio test statistic. The
effectiveness of the proposed procedure is illustrated on synthetic data.
