Change Detection in The Covariance Structure of High-Dimensional Gaussian Low-Rank Models

This paper is devoted to the problem of testing equality between the covariance matrices of L multivariate Gaussian time series with dimension M, in the context where each of the L covariance matrices is the sum of a low-rank K component and the identity matrix. Assuming N 1 , …, N L samples are available for each time series, a new test statistic, based on the eigenvalues of the L sample covariance matrices (SCM) of each time series as well as the eigenvalues of a pooled SCM mixing the N 1 +…+N L available samples, is pro-posed and proved to be consistent in the high dimensional regime in which M, N 1 , …, N L converge to infinity at the same rate, while K and L are kept fixed. Numerical simulations show that the proposed test statistic is competitive with other relevant methods for moderate values of M, N 1 , …, N L .