| Abstract: | We show that the minimal forward (reverse) recursive unit tests of Banerjee, Lumsdaine and Stock Journal of Business and Economics Statistics (1992) Vol. 10, pp. 271–288] are consistent against the alternative of a change in persistence from I(0) to I(1) I(1) to I(0)]. However, these statistics are also shown to diverge for series which are I(0) throughout. Consequently, a rejection by these tests does not necessarily imply a change in persistence. We propose a further test, based on the ratio of these statistics, which is consistent against changes either from I(0) to I(1), or vice versa, yet does not over‐reject against constant I(0) series. Consistent breakpoint estimators are proposed. |
