I've become a bit confused by texts and answers that seem to contradict each other but I think I am just not understanding it quite right.
For an ARMA(p,q) process $$ X_{t} = Z_{t} + \phi(1)X_{t-1} + \dots \phi(p) X_{t-p} + \theta(1)Z_{t-1} + \dots \theta(q)Z_{t-q} $$
I have seen the condition for stationarity being that the roots of $\phi(x)$ are not on the unit circle.
And for $AR(p)$ processes $$ X_{t} = Z_{t} + \phi(1)X_{t-1} + \dots \phi(p) X_{t-p} $$ that they are outside of the unit circle.
A comment in this accepted answer mentions that its stationary but not invertible and it has some upvotes. Yet in my homework problems we have a few that are inside the unit circle and they are not stationary. I also checked them visually and they dont' seem to be.
Yet, an AR(p) process is just an ARMA(p, 0) process, so I don't understand how the conditions could differ?
Any insights are appreciated, I've been reading a lot of different sources trying to understand this and I'm still confused after a few weeks.