I have the following regression

where the dependent variable is I(2), i.e. I need to apply the second order difference to make it stationary.

Now the question would be whether I have to apply the second order difference also to the right hand side of the equation, such that

even if the independent variables are I(0) or I(1), or whether it is fine to just difference the dependent variable while leaving the independent variables unchanged such that my regression looks as follows


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