Hello, I have two sets of time series that I found to be I(1), so I went ahead with using cointegration methods to find a relation between the two variables. Now I'm questioning if the series is trend-stationary, which would mean I'd need a deterministic time trend in my cointegration. I have done the ADF test on the series and found that even when including a time trend there, I still find that the series is non-stationary in level and stationary in first difference. Does this mean my series is not trend-stationary and that my initial approach is still valid? If what I did is wrong, how does one test for trend-stationarity? Thank you.