Optimal fractional dickey-fuller tests for unit roots

Abstract

This article studies the fractional Dickey-Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002). Apart from de analogy with the Dickey-Fully test, the main motivation for their method relies on simulations since these authors do not provide any justification for their particular implementation of the FDF test. In order to give additional rationale to the test, we frame the FDF test in a model where a nuisance or auxiliary parameter is not identified under the null hypothesis. Within this framework we investigate optimality aspects of the class of tests indexed by this auxiliary parameter and show that the test proposed by these authors is not optimal. In addition, we propose feasible FDF test with good asymptotic and finite sample properties.