Efficient Wald tests for fractional unit roots

In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first-order asymptotic properties of the proposed tests are not affected by the preestimation of short or long memory parameters.