A1573
Title: Detecting change-points of univariate time series using the Wasserstein distance
Authors: Anton Imm - RWTH Aachen University (Germany) [presenting]
Fabian Mies - Delft University of Technology (Netherlands)
Ansgar Steland - RWTH Aachen University (Germany)
Abstract: The detection of change-points in univariate nonstationary time series in a nonparametric setting is studied. A statistic based on a truncated Wasserstein distance between localized empirical distribution functions of the time series is introduced, suited to the testing problem. The one-dimensional Wasserstein distance is characterized by the sequential quantile process, and the weak convergence of this process to a Gaussian limit is established. To address the nonlinearity of the quantile process, a new Bahadur representation result is developed, allowing consideration of the asymptotic behavior of the empirical process instead of the quantile process. The proof requires further analysis of the modulus of continuity of the empirical process. For feasible inference, a Gaussian multiplier bootstrap scheme is introduced and its performance is analyzed via a simulation study.
