Extreme Value Theory and heavy (long) tailed distributions 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?
 A: I believe it is true that EVT does not apply to self-similar processes (i.e. processes with dependence, violating iid).  However, not all heavy tailed distributions exhibit dependence. (I say "I believe..." because I don't have expertise in EVT specifically.)
I can suggest several resources that could be helpful, both to answer your question and to offer alternative methods:


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*Introduction to Heavy-Tailed Distributions, Self-Similar Processes, and Long-Range Dependence - http://www.cse.wustl.edu/~jain/cse567-13/ftp/k_38lrd.pdf

*Measures of Deviation (and Dependence) for Heavy-Tailed Distributions and their Estimation under Interval and Fuzzy Uncertainty - http://www.cs.utep.edu/vladik/2011/tr11-07.pdf
Here's a resource about varieties of correlation and dependence, which might help you select a method that is appropriate to the dependence in your data:


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*CORRELATION AND DEPENDENCE IN RISK MANAGEMENT: PROPERTIES AND PITFALLS - ftp://ftp.sam.math.ethz.ch/pub/risklab/papers/CorrelationPitfalls.pdf
