  In this paper we derive closed-form formulas of feedback capacity and
nonfeedback achievable rates, for Additive Gaussian Noise (AGN) channels driven
by nonstationary autoregressive moving average (ARMA) noise (with unstable one
poles and zeros), based on time-invariant feedback codes and channel input
distributions. From the analysis and simulations follows the surprising
observations, (i) the use of time-invariant channel input distributions gives
rise to multiple regimes of capacity that depend on the parameters of the ARMA
noise, which may or may not use feedback, (ii) the more unstable the pole
(resp. zero) of the ARMA noise the higher (resp. lower) the feedback capacity,
(iii) certain conditions, known as detectability and stabilizability are
necessary and sufficient to ensure the feedback capacity formulas and
nonfeedback achievable rates {\it are independent of the initial state of the
ARMA noise}. Another surprizing observation is that Kim's \cite{kim2010}
characterization of feedback capacity which is developed for stable ARMA noise,
if applied to the unstable ARMA noise, gives a lower value of feedback capacity
compared to our feedback capacity formula.
