Recently, I received an email from a follower of this blog, who asked:
"May I know what is the difference between the bandwidth of Newey-West and Andrews for the KPSS test. It is because when I test the variable with Newey-West, it is I(2), but then I switch the bandwidth to Andrews, it becomes I(1)."
First of all, it's worth noting that the unit root and stationarity tests that we commonly use can be very sensitive to the way in which they're constructed and applied. An obvious example arises with the choice of the maximum lag length when we're using the Augmented Dickey-Fuller test. Another example would be the treatment of the drift and trend components when using that test, So, the situation that's mentioned in the email above is not unusual, in general terms.
Now, let's look at the specific question that's been raised here.