The power properties of the rank-based Dickey-Fuller (DF) unit root test of Granger and Hallman [C. Granger and J. Hallman, Nonlinear transformations of integrated time series, J. Time Ser. Anal. 12 (1991), pp. 207-218] and the range unit root tests of Aparicio et al. [F. Aparicio, A. Escribano, and A. Siplos, Range unit root (RUR) tests: Robust against non-linearities, error distributions, structural breaks and outliers, J. Time Ser. Anal. 27 (2006), pp. 545-576] are considered when applied to near-integrated time series processes with differing initial conditions. The results obtained show the empirical powers of the tests to be generally robust to smaller deviations of the initial condition of the time series from its underlying deterministic component, particularly for more highly stationary processes. However, dramatic decreases in power are observed when either the mean or variance of the deviation of the initial condition is increased. The robustness of the rank- and range-based unit root tests and their higher power results relative to the seminal DF test have both been noted previously in the econometrics literature. These results are questioned by the findings of the present paper.
