Let's assume we have 2 variables and test each of them for a unit root with the ADF test. When plotting the data, we can see that it has some up/down movements but is overall clearly trending upwards.
At level, variable A is stationary with "no constant", "constant" and "constant+trend" (p<0.05). Variable B is only stationary with "constant+trend" (p<0.05).
At first differences, both variables are stationary at "no constant", "constant" and "constant+trend" (p<0.05).
Is it o.k. to conclude that Variable A and B are both integrated of the same order I(1), or do we have to assume that Variable B is I(0) with respect to a trend and Variable B is I(1)?
I want to conduct a Johansen Cointegration test and after reading the literature and several posts, I'm still not sure if it's okay test for correlation with the data at level (and a trend).