Self-normalised change point tests that remain pivotal under non-stationarity

Self-normalising test statistics for time series circumvent the lag-specification of long-run variance estimators by employing an inconsistent estimator for studentization. This leads to asymptotically pivotal test distributions under stationarity, but not for nonstationary sequences. Focusing on the multiple changepoint problem, we propose an alternative self-normalised test statistic which is asymptotically pivotal even if the noise is nonstationary. Central to our argument are statistical functionals which are invariant under temporal reparametriation, i.e. clock-changes. Simulations show that the proposed procedure is more conservative than competing bootstrap procedures, but considerably more powerful against multiple changes and more reliable in terms of size for highly nonstationary time series in larger samples.