Whenever we test the stationarity of our time-series data we use a "complete" historical time-series. That's to say, there can't be any "gaps" in the series,arising perhaps due to data observations that were not recorded, are contaminated, or are such extreme outliers that they are unbelievable and have to be discarded.
If observations are missing, for whatever reason, then we can't apply standard tests such as the Augmented-Dickey-Fuller (ADF) test, or the Kwiatowski, Phillips, Schmidt and Shin (KPSS) test.
Or can we?
