Robust Dickey–Fuller tests based on ranks for time series with additive outliers

In this paper the unit root tests proposed by Dickey and Fuller (DF) and their rank counterpart suggested by Breitung and Gouriéroux (J Econom 81(1): 7–27, 1997) (BG) are analytically investigated under the presence of additive outlier (AO) contaminations. The results show that the limiting distribution of the former test is outlier dependent, while the latter one is outlier free. The finite sample size properties of these tests are also investigated under different scenarios of testing contaminated unit root processes. In the empirical study, the alternative DF rank test suggested in Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) (GH) is also considered. In Fotopoulos and Ahn (J Time Ser Anal 24(6): 647–662, 2003), these unit root rank tests were analytically and empirically investigated and compared to the DF test, but with outlier-free processes. Thus, the results provided in this paper complement the studies of the previous works, but in the context of time series with additive outliers. Equivalently to DF and Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) unit root tests, the BG test shows to be sensitive to AO contaminations, but with less severity. In practical situations where there would be a suspicion of additive outlier, the general conclusion is that the DF and Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) unit root tests should be avoided, however, the BG approach can still be used.