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I have annual data with 25 observations. 1 dependent variable and 4 independent variables. I used to methods to test stationarity. First I de-trended data and used ADF test and found out that all my variables became stationarity at level I(0) after de-trending. I also directly applied ADF to all the variables but then some became stationary at first difference, some at level and some at second difference. Now, I am confused which stationarity criteria to take for further analysis. And depending on whichever approach I take, what model should then I apply to estimate the parameters?

P.S:- Also, I applied johanssen-cointegration test on my original data and found that variables are con-integrated of order 2. That is, 5-3=2.

Help needed urgently. thanks

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You can consider "VAR in levels". There are a lot of papers based on level variables, especially when you rely on the results of impulse responses. for example refer to Smets and Peersman (2001; pdf) you can also seasonally adjust series before checking unit root test.

Full reference:

  • Peersman, G., & Smets, F. (2001). The monetary transmission mechanism in the euro area: more evidence from VAR analysis (MTN conference paper).
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