  While many methods are available to detect structural changes in a time
series, few procedures are available to quantify the uncertainty of these
estimates post-detection. In this work, we fill this gap by proposing a new
framework to test the null hypothesis that there is no change in mean around an
estimated changepoint. We further show that it is possible to efficiently carry
out this framework in the case of changepoints estimated by binary segmentation
and its variants, $\ell_{0}$ segmentation, or the fused lasso. Our setup allows
us to condition on much less information than existing approaches, which yields
higher powered tests. We apply our proposals in a simulation study and on a
dataset of chromosomal guanine-cytosine content. These approaches are freely
available in the R package ChangepointInference at
https://jewellsean.github.io/changepoint-inference/.
