Regression‐based Tests for a Change in Persistence *

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.