Nonparametric change point detection in multivariate piecewise stationary time series

Detecting change points in multivariate time series is an important problem with numerous applications. We develop a nonparametric method to detect multiple change points in multivariate piecewise stationary processes when the locations and number of change points are unknown. Based on a test statistic that measures differences in the spectral density matrices through the norm, we sequentially identify points of local maxima in the test statistic and test for the significance of each of them being change points. In addition, the components responsible for the change in the covariance structure at each detected change point are identified. The asymptotic properties of the test for significant change points under the null and alternative hypothesis are derived. We illustrate the better performance of our method in comparison to some of the recent methods through a few simulation examples and discuss applications of our method in seismology and finance.