Resnick, S.

1=2 process value distribution hill plot order theorem probability statistic resnick number j g dt university extremal figure estimate pareto gamma limit arch process variable index condition estimator hill estimator proof pareto distribution su ciently sequence extremal index result order statistics althill plot sample brownian motion rootzen table alt plot 1= log n uniform convergence theorem erasmus university rotterdam equation function 1 i n althill =kn 1 t jn i ln 1 peraltkn 1=2 perhill rotterdam logln estimation 1998. 1.0 0.8 0.6 convergence 0.4 ciently point stric exceedance method research log n log i perhillkn 1=2 +1=sj peraltkn neighborhood i.i.d bollerslev 0.2 0.000 poisson motion simulation engle 1997. solution