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Advisor(s)
Abstract(s)
The extremal index is an important parameter in the characterization of extreme values of a
stationary sequence. Our new estimation approach for this parameter is based on the extremal
behavior under the local dependence condition D(k)(un). We compare a process satisfying one of
this hierarchy of increasingly weaker local mixing conditions with a process of cycles satisfying the
D(2)(un) condition. We also analyze local dependence within moving maxima processes and derive
a necessary and su cient condition for D(k)(un). In order to evaluate the performance of the proposed
estimators, we apply an empirical diagnostic for local dependence conditions, we conduct a
simulation study and compare with existing methods. An application to a nancial time series is
also presented.
Description
Keywords
Extreme value theory Stationary sequences Dependence conditions Extremal indexion