I have a question on testing for stationarity with the ADF test, in order to determine the order of integration.
We do have a time series that looks in plot(df) obviously trending at level and has a high fluctuation ("drift+trend"). We therefore assume, that we have to apply following script from vars to get an appropriate ADF test result:
ur.df(df, type = "trend", selectlags = "BIC")
Assume the test finds that the time series is not stationary (,as the plot already suggested). We therefore proceed testing the first difference of the time series:
ur.df(diff(df), type = "trend", selectlags = "BIC")
Is it okay to consider "trend" in the test, when we know that diff(df) looks stationary in plot(diff(df)?