Improving the length of confidence sets for the date of a break in level and trend when the order of integration is unknown

•We consider confidence sets for the timing of a break in level and/or trend.•The confidence sets employ modified weighting schemes for the break magnitudes.•The new confidence sets have shorter length but retain accurate coverage.

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.