Testing the Fractional Integration Parameter Revisited: a Fractional   Dickey-Fuller Test
  In this paper, in the first step, we show that the fractional Dickey-Fuller test proposed by Dolado et al [10] is useless in practice. In the second step, we propose a new testing procedure for the degree of fractional integration of a time series inspired on the unit root test of Dickey-Fuller [7]. Through a simulation study, we show the good performance of the test in terms of size and power. Finally, in order to show how to use the new testing procedure, the test is applied to the well-known Nelson and Plosser data. 
Ahmed Bensalma and Mohamed Bentarzi
math.ST stat.TH