A consistent test for unit root against fractional alternative

Sowell (1990) found that the fractional unit root distribution pose problems when testing for unit root. In this note, by means of reinterpretation and generalization of Sowell's results we show that a pure fractionally integrated processes of order d, (FI(d)), with d ∈ R, are not explosive. By using the non explosive feature of F I(d) processes, we build a new testing hypotheses for unit root, which make that the fractional unit root distributions are robust for any misspecification in order of integration.