# How to apply second order differencing to time-series regression?

I have the following regression

$y_{t}&space;=&space;\alpha_t&space;+&space;\beta_t&space;X_t&space;+&space;\epsilon_t$

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

$\Delta^2y_{t}&space;=&space;\Delta^2\alpha_t&space;+&space;\Delta^2(\beta_t&space;X_t)&space;+&space;\Delta^2{\epsilon_t}$

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

$\Delta^2y_{t}&space;=&space;\alpha_t&space;+&space;\beta_t&space;X_t&space;+&space;\epsilon_t$