Unbiased Tail Estimation by an Extension of the Generalized Pareto Distribution
CentER Discussion Paper No. 2005-112
17 Pages Posted: 14 Nov 2005
Date Written: October 21, 2005
The generalized Pareto distribution (GPD) is probably the most popular model for inference on the tail of a distribution. The peaks-over-threshold methodology postulates the GPD as the natural model for excesses over a high threshold. However, for the GPD to fit such excesses well, the threshold should often be rather large, thereby restricting the model to only a small upper fraction of the data. In case of heavy-tailed distributions, we propose an extension of the GPD with a single parameter, motivated by a second-order refinement of the underlying Pareto-type model. Not only can the extended model be fitted to a larger fraction of the data, but in addition is the resulting maximum likelihood for the tail index asymptotically unbiased. In practice, sample paths of the new tail index estimator as a function of the chosen threshold exhibit much larger regions of stability around the true value. We apply the method to daily log-returns of the euro-UK pound exchange rate. Some simulation results are presented as well.
Keywords: bias reduction, exchange rate, heavy tails, peaks-over-threshold, regular variation, tail index
JEL Classification: C13, C14
Suggested Citation: Suggested Citation