Harvey and Leybourne (2015) construct confidence sets for the timing of a break in level and/or trend, based on inverting sequences of test statistics for a break at all possible dates. These are valid, in the sense of yielding correct asymptotic coverage, for I(0) or I(1) errors. In constructing the tests, location-dependent weights are chosen for values of the break magnitude parameter such that each test conveniently has the same limit null distribution. By not imposing such a scheme, we show that it is generally possible to significantly shorten the length of the confidence sets, whilst maintaining accurate coverage properties.
Harvey, D. I., & Leybourne, S. J. (in press). Improving the length of confidence sets for the date of a break in level and trend when the order of integration is unknown. Economics Letters, 145, https://doi.org/10.1016/j.econlet.2016.06.015