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.