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It would be highly inefficient to perform estimates merely on a few extreme values. If one estimates parameters using all threshold exceedances however, then there's a lot more data available to use. That's the idea anyway, together with the fact that the possible asymptotics belong to on of three families of EV distributions: Gumbel, Frechet or Negative Weibull.

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Mon Sep 22nd, 2008 at 05:00:21 AM EST
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