This paper deals with a fractionally integrated, FI(d), processes {yt, t = 1,… , n}, where the fractional integrated parameter d is any real number greater than 1/2. We show, for these processes, that the suitable hypotheses test for unit root are H0: d ≥ 1 against H1inf>: d < 1. These new hypotheses test can be considered as a test for unit root against fractional alternative. The asymptotic distributions under the null and alternative generalise those obtained by Sowell (1990). Monte‐Carlo simulations show that the proposed test is robust for any missepecification of the order of integration parameter d and that it fares very well in terms of power and size. The paper ends with empirical applications by revisiting Nelson‐Plosser Data.
