Overall, the M-tests has the smallest size distortion, with the ADF t test having the next smallest. The ADF -test, , and have the worst size distortion. In addition, the power of the DF-GLS and M-tests are larger than that of the ADF t test and -test. The ADF has more severe size distortion than the ADF , but larger power for a fixed lag length. Ignoring this complication, though, the process for performing an ADF test in Stata is no different from performing the standard DF test. In fact, the command is the same. You must simply add a certain number of lagged differences via lags( k) as an option to dfuller. For example, an ADF for an AR(2) vs a random walk is dfuller X, nocons lags( 1). There are two different approaches: stationarity tests such as the KPSS test that consider as null hypothesis H0 that the series is stationary, and unit root tests, such as the Dickey-Fuller test and its augmented version, the augmented Dickey-Fuller test (ADF), or the Phillips-Perron test (PP), for which the null hypothesis is on the contrary 3. KPSS Test: A widely used test in econometrics is Kwiatkowski-Phillips-Schmidt-Shint or abbreviated as the KPSS test. This test is pretty similar to ADF too and can help to validate the null hypothesis that an observable time series is stationary around a deterministic trend. Regarding the PP (Newey-West correction) and KPSS tests versus the DF-GLS then I would go with the DF-GLS (since it is more efficient than the PP) but I would also implement the tests below. I remember reading a paper on the KPSS test saying that it basically has a similar problem of low power which the SDF and PP test have but I cannot find it. Usually I start with thinking about/reading about/researching the nature of my variables very carefully. If I felt I had to test for some reason, I'd try to avoid testing the specific data I needed a model for, but other, closely related data (e.g. same variable in a different time span, similar/closely related variables etc) .

kpss test vs adf test