Rank-based multiple change-point detection in multivariate time series

In this paper, we propose a Bayesian approach for multivariate time series segmentation. A robust non-parametric test, based on rank statistics, is derived in a Bayesian framework to yield robust distribution-independent segmentations of piecewise constant multivariate time series for which mutual dependencies are unknown. By modelling rank-test p-values, a pseudo-likelihood is proposed to favour change-points detection for significant p-values. A vague prior is chosen for dependency structure between time series, and a MCMC method is applied to the resulting posterior distribution. The Gibbs sampling strategy makes the method computationally efficient. The algorithm is illustrated on simulated and real signals in two practical settings. It is demonstrated that change-points are robustly detected and localized, through implicit dependency structure learning or explicit structural prior introduction.