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

The problem of quantifying uncertainty about the locations of multiple change points bymeans of confidence intervals is addressed. The asymptotic distribution of the change pointestimators obtained as the local maximisers of moving sum statistics is derived, wherethe limit distributions differ depending on whether the corresponding size of changes islocal, i.e. tends to zero as the sample size increases, or fixed. A bootstrap procedure forconfidence interval generation is proposed which adapts to the unknown magnitude ofchanges and guarantees asymptotic validity both for local and fixed changes. Simulationstudies show good performance of the proposed bootstrap procedure, and some discussionsabout how it can be extended to serially dependent errors are provided.