I have a set of time series which exhibits no autocorrelation but the variance is not constant.
I remember that one of the requirements of cross-correlation to be meaningful is weak stationarity (we use a constant mean and variance in its computation).
In my case, I'm trying to find similar groups of time series, if I use cross-correlation to measure their similarity, two time series will be similar if they follow similar geometric profiles over time, independently of their magnitude. I think that alone makes sense without requiring stationarity.
Can I use it for the time series above and obtain meaningful results in terms of similar geometric profiles? I think stationarity would be only required if I wanted to use the cross-correlation for other inferential purposes. Is this reasoning correct?