As far as I know, the CUSUM algorithm is meant for detecting change points on discrete-time uncorrelated random processes.
For instance, to apply the CUSUM algorithm to a discrete Gaussian process, we must know for sure that each sample is statistically independent from the others. I have seen this assumption in the CUSUM algorithm demonstration.
However, I have not found the CUSUM alternative for a discrete-time correlated random process. Let's say, for a realization of a band-pass filtered Gaussian process $X[n]$ with a changing variance at a certain sample $n_c$.
What to do in such a scenario? Can I still apply CUSUM?