Unit Root Testing under a Local Break in Trend using Partial Information on the Break Date

We consider unit root testing allowing for a break in trend when partial information is available regarding the location of the break date. This takes the form of knowledge of a relatively narrow window of data within which the break takes place, should it occur at all. For such circumstances, we suggest employing a union of rejections strategy, which combines a unit root test that allows for a trend break somewhere within the window with a unit root test that makes no allowance for a trend break. Asymptotic and finite sample evidence shows that our suggested strategy works well, provided that, when a break does occur, the partial information is correct. An empirical application to UK interest rate data containing the 1973 oil shock' is also considered.