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

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Abstract

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

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