On Adaptive Tail Index Estimation for Financial Return Models
UC Berkeley Working Paper No. RPF-295
31 Pages Posted: 23 Jan 2001
Date Written: January 2002
Abstract
Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator's performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.
Keywords: Fat-tails, tail index of stationary marginal distributions, Hill estimator, minimal AMSE
JEL Classification: C13, C14
Suggested Citation: Suggested Citation
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