Assumption of independence observations over time

[usercluster]

Good morning,
I find this methods very interesting, but looking at the original paper, and also at the theory behind the previous version of the technique (in the package 'ecp'), I see that there is the assumption of independent observations over time, which is quite restrictive in the context of time series. How would you suggest to deal with that? I checked and some of the examples proposed do not actually perfectly follow this assumption since there is some autocorrelation in the data.
Thank you