I(0) , I(1)

[hxh]

Hello

I have a question towards the order of Intergration.

If I have a time series which is showing a trend , this trend can be determenistic or stochastic. This I dont know from just looking at the graph.
No I am gonna make Unit Root tests to determine the ORder of Integration.

Assume that I find that the first differences have no unit root.

So first I test the series without including a trend and the test result is that there is a unit root. This would mean that the process is I(1).

Ok but when I include a trend term in the test I find that there is no unit root, which means that the process is trend stationary.
Can i now say that the process is I(0) ??

Do I think correct ?

best regards