In this note we show that, when the true data generating process is a
stationary one around a constant term with a break, the stationarity test
of Kim (2000, Journal of Econometrics
95, 97–116) against the alternative hypothesis of change of
persistence rejects the null of stationarity asymptotically with
probability one.I am grateful to an
anonymous referee for his useful comments, which have helped to improve
the content and presentation of this note. I acknowledge financial support
from Ministerio de Ciencia y Tecnología, project
SEC2003-09205.