Cross section regression + Stationarity + ML : big question


I have a question: can we regress non stationary data in cross section regressions?
If not, can we use them in ML models?
I cannot find easy response

Thank you !!!

You'll have to give a much more specific question to get a meaningful answer.


You are right, thank you ! Let me rephrase differently the question please:

Database organised in cross-section:
Variable Y Variable X1 Variable X2
Price Company A Feature 1 Feature 2
Price Company B Feature 1 Feature 2
Price Company C Feature 1 Feature 2

Regression Y (price of a company) on its X (features of company).
It is not a time series, so i wonder if the requirement of stationarity holds. Even if i standardize the data, it does not change the unit root tests.
Question: what is the solution to do regression in cross section in presence of unit root?
Thanks a lot.

If I understand correctly, the left hand side variable is nonstationary and all the right hand side variables are stationary. That can't work.

Would it make sense in your application for the LHS variable to be returns rather than price?

Thank you for reply.
I'm sorry i might have not been clear.
My concern was general. Some variables are stationnary and other not. In my case, LHS are stationnary (dependent var) and RHS some have unit root, other not.
Just forget the price, imagine a generic variable. It is a cross section data because all occur in same period so no returns (data are anonymized..).

I had missed that it was cross-section data. If there is no time-series aspect, it doesn't matter whether some of the variables are nonstationary. You should be good.

Many thanks for your reply.
Right, there is no time series, no panel, only cross section (it's not my fault, data are like this), so i thought like you but had difficulty to find theoretical references if any as most of the references are on TS and Panel. So please if any reference, would enjoy read it although like you i don't see the need to see stationarity on CS.