I want to apply an ARDL model to a data set of 5 yearly time series (one response and 4 explanatory), spanning from 1971 to 2014. After some research, I found that an ARDL model requires each series to be either I(0) or I(1), therefore a unit root test is necessary. However, when I run the Augmented Dickey-Fuller test in R, I obtain some conflicting results. For example, I have the following series (EI.png). When I run the following test, I obtain results suggesting the presence of a unit root both at the levels and at the differences (TEST1.png):
But when I run the same test on the difference series, the results suggest the absence of a unit root (TEST2.png).
Again, when I put type = "trend", the test shows there is no unit root (TEST3.png).
Can someone please help me understand which of these tests I should report when writing my paper? Can I report a series as stationary if it is trend-stationary? Thank you in advance.
PS: These are all the remaining four series (All.png):
Thank you very much Mr Adeyemo for your reply.
I am using the ARDL procedure since it is the most implemented method in the literature for the kind of relationships I am trying to assess, especially in the case of a single country (as opposed to a panel of countries).
I tried the other tests you mentioned (PP, KPSS) and even ZA and ADF-GLS, and they all reject the null hypothesis of the existence of a unit root once I choose to add a trend to the test. I am intending to be honest about it, and I hope it does not pose a problem to the reviewers.
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