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Continuous-Time Tail Index Estimation

Author
Milanovici, Florian
Abstract
In applications to finance, insurance, physics and
many other fields, statisticians are often faced with high quality
datasets that exhibit deviations from the "normal behavior", caused
by the extremes in the sample. As a consequence in recent years a
great deal of research has been done in heavy-tailed modelling.
Although much of the existing literature focuses on the
discrete-time case, the continuous-time heavy-tailed modelling is a
very natural technique in many applications and therefore more
attention should be paid to the continuous-time case. This is the
motivation for the research in this dissertation. We will be
focusing mainly on extending the Hill estimator (Hill (1975)) to
estimating the tail index of continuous-time stationary stochastic
processes. Since one can sample basically as many observations as
possible from the continuous-time process, there is a temptation on
the practitioner's part to use as large a sample as possible when
applying the Hill estimator. We will show that this will lead in
many instances to asymptotically inconsistent estimators.
Date Issued
2006-10-17Subject
Hill estimator; heavy-tailed
Type
dissertation or thesis