Detecting change-points in multidimensional stochastic processes

A general test statistic for detecting change-points in multidimensional stochastic processes with unknown parameters is proposed. The test statistic is specialized to the case of detecting changes in sequences of covariance matrices. Large-sample distributional results are presented for the test statistic under the null hypothesis of no-change. The finite-sample properties of the test statistic are compared with two other test statistics proposed in the literature. Using a binary segmentation procedure, the potential of the various test statistics is investigated in a multidimensional setting both via simulations and the analysis of a real life example. In general, all test statistics become more effective as the dimension increases, avoiding the determination of too many “incorrect” change-point locations in a one-dimensional setting.