Say I specify an AR(2) process as $X_t = 0.5 + 0.7X_{t-1} + 0.4X_{t-2} + e_t$. I would not expect this process to be covariance stationary. Indeed, if I project this series stochastically, it grows very quickly.
The characteristic polynomial is, I think, $0.5 - 0.7z - 0.4z^2=0$. The roots of this equation are, I think, $-2.29$ and $0.54$. These roots lie outside the unit circle. Which suggests that the process is covariance stationary. Where am I going wrong?
I unfortunately don't have literature here.
However, I have the following in my mind: the sum of the coefficients equals $1.1 \geq 1,$ such that your time-series doesn't necessarily has to be stationary. I could imagine that there's an implication if the sum is greater 1 (no stationary solution) and that there's an implication if the sum is equal 1 (Integrated AR(2)-model.)
Excuse my vague answer.