This article compares the asymptotic power properties of the Wald, the Lagrange Multiplier and the Likelihood Ratio test for fractional unit roots. The paper shows that there is an asymptotic inequality between the three tests that holds under fixed alternatives.

This article studies the fractional Dickey- Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002). Apart from the analogy with the Dickey-Fuller test, the main motivation for their method relies on simulations since these authors do not provide any...