Work

Change-point detection in low-rank VAR processes

Year: 2025

Type: article

Abstract: 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 the 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 method is demonstrated using both synthetic and real data.

Source: Bernoulli

DOI: 10.3150/24-bej1760

Authors: Farida Enikeeva, Olga Klopp, Mathilde Rousselot