After reading about AR(p) processes I have one question regarding the characteristic polynomial of AR(p) processes and its roots.
Let's say that you want to determine whether the time series
$$y_t = \frac{1}{5} y_{t-1} + 3\pi + \epsilon_t$$
is stationary. Then you would set up the characteristic polynomial of this AR(p) process and consider the roots. Formally, I know how it works with introducing some lag operator $L$.
My question is about the importance of the constants. Does $3\pi$ matter or could I just write $3\pi + 2017$ and the characteristic polynomial would still be the same? I thought it would be okay since you can define
$$\tilde{\epsilon}_t = 3\pi + \epsilon_t$$ but I am not sure this is alright.
EDIT:
Also, there is a similiar question with regard to the time series
$$y_t = \frac{1}{5} y_{t-1} + 3\pi + 2\epsilon_t$$
Does the doubled white noise have any influence with regard to stationarity?