When testing the stationarity of residuals after OLS estimation, the ADF and KPSS test have opposing conclusions when it comes to rejecting the null:
- ADF: Rejection of null concludes evidence of stationarity
- KPSS: Rejection of null concludes evidence of non-stationarity.
In addition, the sample size is fairly low (approx 40 observations). Is this what's throwing off the test? From what I've read ADF has low power as well. In such a situation would it be appropriate to use DF-GLS instead?