Below, we display two AR(1)'s with the same unconditional variance. One has very slow-decaying stochastic volatility that is an AR(1) with unconditional mean 10, while the other has constant variance of 10 (note that it would be hard to tell this from the second diagram! We offer a random draw of results).
First, the values with and without stochastic volatility (click to enlarge).
And our stochastic variance terms in our AR(1) (click to enlarge):