Continuous-Time Tail Index Estimation
In applications to finance, insurance, physics andmany other fields, statisticians are often faced with high qualitydatasets that exhibit deviations from the "normal behavior", causedby the extremes in the sample. As a consequence in recent years agreat deal of research has been done in heavy-tailed modelling.Although much of the existing literature focuses on thediscrete-time case, the continuous-time heavy-tailed modelling is avery natural technique in many applications and therefore moreattention should be paid to the continuous-time case. This is themotivation for the research in this dissertation. We will befocusing mainly on extending the Hill estimator (Hill (1975)) toestimating the tail index of continuous-time stationary stochasticprocesses. Since one can sample basically as many observations aspossible from the continuous-time process, there is a temptation onthe practitioner's part to use as large a sample as possible whenapplying the Hill estimator. We will show that this will lead inmany instances to asymptotically inconsistent estimators.
Year of publication: |
2006-10-17
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Authors: | Milanovici, Florian |
Subject: | Hill estimator | heavy-tailed |
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