@whuber What I mean is, I have heard that the AR coefficients cannot be equal nor bigger than 1, and as far as I know there are some exceptions from it. The problem is, I'm not sure how to prove it while having an actual example.

As mentioned above, most likely it's a random process. Check it for seasonality, but I wouldn't expect much. Nevertheless, if modeling this exact series is important for any reason, I would check for nonlinearities in the series, might appear to be some sort of threshold model.

@mlofton also, how would you define sufficient condition for stationarity in practice?

@mlofton thanks for the answer! However, as far as I understand the ADF structure, the test actually creates an AR model, which means it is somehow possible for it to represent that process as (cov(x,y)/var(x)) in order to get the coefficients. Does that mean it's overfitting it on purpose? And more interestingly, as you say 'not finding a unit root is not sufficient' - what would your recommendation be to confirm covariance stability?

Thank you, I misunderstood the intention. In such case, overdifferencing stationary time series might lead to poor accuracy, instead of that it's worth checking, if simply differencing the nonstationary series and including them in VAR altogether will work. Running several autocorrelation tests is imperative. If that doesn't work, I would suggest using hybrid models or 2 steps approach. It is unclear to me however how the relationships between the series have been determined (e.g. is there any cointegration?), so it's rather difficult to give a straightforward answer.