Bootstrap confidence intervals for multiple change points based on moving sum procedures

In this work, we address the problem of quantifying uncertainty about the locations of multiple change points. We first establish the asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum statistics, where the limit distributions differ depending on whether the corresponding size of changes is local, i.e. tends to zero as the sample size increases, or fixed. Then, we propose a bootstrap procedure for confidence interval generation which adapts to the unknown size of changes and guarantees asymptotic validity both for local and fixed changes. Simulation studies show good performance of the proposed bootstrap procedure, and we provide some discussions about how it can be extended to serially dependent errors.