I have read somewhere (possibly in Hayashi's Econometrics text) that it can be problematic to work with differenced trend-stationary processes. I have not been able to find the exact source again and I do not remember in which context this was stated to be problematic. Can someone make sense of this?
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See https://stats.stackexchange.com/questions/461594/is-a-time-trend-a-substitute-for-first-differencing (and its links!) – kjetil b halvorsen Jul 19 '20 at 22:42