Showing a dual relationship between ARIMA (0,2,1) with parameter θ=-1 and the random walk, a new alternative hypothesis in the form of ARIMA (0,2,1) is established in this paper for evaluating unit root tests. The power of four methods of testing for a unit root is investigated under the new alternative, using Monte Carlo simulations. The first method testing θ=-1 in second differences and using a new set of critical values suggested by the two authors in finite samples, is the most appropriate from the integration order point of view.
