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...

We consider changes in the degree of persistence of a process when the degree of persistence is characterized as the order of integration of a strongly dependent process. To avoid the risk of incorrectly specifing the data generating process we employ local Whittle estimates which uses only...