Unit Root Tests for Long Memory Series in the Presence of Structural Breaks in Variance

This paper extends the unit root tests to long memory observations in the existence of variance breaks. Given for the case of non-constant variance, the asymptotic properties of commonly used unit root tests are derived under the null hypothesis. It is shown that the non-constant variance can both inflate and deflate the rejection frequency, thus the statistic tests are not robust. The simulation results also indicate the extent of size distortion is heavily sensitive to the location and magnitude of change points, long memory index and sample size.