Testing for a Structural Break at Unknown Date with Long-memory Disturbances.

We derive the null limiting distributions of the usual sup-Wald and CUSUM tests for structural stability with an unknown potential break date in a polynomial regressi on model where the errors are I(d), -0.5 < d < 0.5. For d > 0, both tests diverge under the null so that the asymptotic size of either test is unity. For d< 0, both tests converge to zero under the null so that the asymptotic size of either test is zero [ABSTRACT FROM AUTHOR]