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I am quite new with timeseries and in my understanding I perceive some contradictions in KPSS and ADF tests combined.

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Using this timeseries when performing ADF and KPSS I could interpret

KPSS: The timeseries fails to reject the null hypothesis of stationarity (wtf? how can this timeseries be stationary if it clearly has a tendency upwards?)

ADF: Can't reject tau (at 1%) and therefore there is a unit root, reject phi2 and therefore there must be drift, trend or both. Can't reject phi3 and this time series would be a randomwalk with drift.

enter image description here enter image description here

How can this timeseries be stationary and have a unit root?

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Statistical tests are not bullet proof. Both the ADF and KPSS test have their limitations. See this answer for example. In my experience it is not uncommon to see conflicting results with these tests. Unfortunately, statistics is hard, there is no one size fits all recipe. In your case, given your plot and that economic variables are historically known to be I(1) or I(2), I would suggest proceeding under the assumption that your variable is not (trend)stationary.

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