when you for a useful model the residuals should have constant variance i.e. not dependent on level and not autoregressive in nature. Thus the residuals need to have homogenous error variance. If the residuals have a predictable variance then one needs to either segment the data ala the CHOW test or to determine a suitable power transform via a BOX-COX power transform.
If you wish you can post an actual time series and I might be able to help further.