Statistical Analysis of Conditional Hill Estimator

Specialeforsvar: Laurits Glargaard

Titel: Statistical Analysis of Conditional Hill Estimator

Abstract: We construct a conditional Hill estimator and show it is consistent under \alpha-mixing and asymptotically normal under beta-mixing. This is done by drawing on methods from non-parametric regression and analysis of Heavy-Tailed Time Series. We show the asymptotic normality of the conditional Hill estimator, unlike the non-conditional case, doesn't require assumptions on the joint extremes. This also means the asymptotic variance is easily calculated. We use the conditional Hill estimator to show the negative tail index of the S&P500 is dependent of the VIX though the structure is difficult to explain.

Vejleder: Martin Bladt
Censor:   Anders Rønn-Nielsen, CBS