Extension of the Unit Root Test: The Fractional Augmented Dickey-Fuller Test A Monte Carlo Study

ABSTRACT Usually we use the Dickey-Fuller test for testing stationarity in a time series under the hypotheses H 0 : I (1) (presence of unit root) versus H 1 : I (0) (absence of unit root), and it is used in the case of a short memory. In this article, we propose an extension of the fractional Dickey-Fuller test proposed by Bensalma used in the long memory case and when the errors of test regression are autocorrelated. The proposed test is considered as a generalization of ADF test and they have the same steps. The asymptotic properties of this test are derived and it is studied by Monte Carlo simulation experiment. The paper ends with an application to illustrate the usefulness and the simplicity of the proposed technique