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.

翻译：向量自回归（VAR）模型广泛应用于多元时间序列分析，用于描述数据的短期动态特性。在处理高维且高度相关的时间序列时，降秩VAR模型尤为重要。这些模型的许多结论基于平稳性假设，但在数据出现结构性突变的多项应用中，该假设并不成立。我们考虑一种低秩分段平稳VAR模型，其中观测过程的转移矩阵可能存在变化。我们提出了一种新的检验方法，用于检测转移矩阵中是否存在变点，并证明了该方法在维度和样本量方面的极小化最优性。我们的两步变点检测策略基于构建转移矩阵的估计量，并将其应用于惩罚似然比检验统计量中。通过合成数据验证了所提方法的有效性。