Nuisance-parameter-free changepoint detection in non-stationary series

Abstract

Many changepoint detection procedures rely on the estimation of nuisance parameters (like long-run variance). If a change has occurred, estimators might be biased and data adaptive rules for the choice of tuning parameters might not work as expected. If the data are not stationary, this becomes more challenging. The aim of this paper is to present two changepoint tests, which involve neither nuisance nor tuning parameters. This is achieved by combing self-normalization and wild bootstrap. We investigate the asymptotic behavior and show the consistency of the bootstrap under the hypothesis as well as under the alternative, assuming mild conditions on the weak dependence of the time series. As a by-product, a changepoint estimator is introduced and its consistency is proved. The results are illustrated through a simulation study. The new completely data-driven tests are applied to real data examples from finance and hydrology.