It seems that choosing the appropriate model for a mix of I(1) and I(0) variables is an hot topic on Stack Exchange but I was not able to find the solution I am looking for :
Considering a TS model with an I(1) dependent variable (y) and an I(0) explanatory variable (x),
- a model of VAR cannot be selected because y is non-stationary.
- a model of VECM is not appropriate since x is stationary. (*I have seen that I can add an explanatory variable which is non stationary I(1) in order to compute a VECM but this not possible in my case).
Is an ARDL model the best way to deal with my data ?
Is it possible to differentiate only the dependent variable y to compute a model of VAR?