I'm analyzing data about which I have a strong suspicion that it is self-similar (Hurst parameter ranging from 0.60 to 0.78 depending on estimation method and sample sequence). I also observe high realization values much more often (compared to experiments where no self-similarity is suspected) which suggests that the generating distribution can have a long (heavy) tail.
It seems that Extreme Value Theory cannot be used in this case to reason about the tail behavior. In case of self-similarity long range dependence does obviously violate the i.i.d. requirement, but does the inability to use EVT in my case apply more broadly to all long tailed distributions?