when you have 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.

After a visual review of the data plot it appears that that the model error variance has increased over time BUT only an analysis of the original data could test that hypothesis. The simple variance of the observed series i.e. a simple mean model appears to have dampened BUT what is of concern is the error variance from a useful auto-projective model or a deterministic model containing trends or level shifts.