Unbiased Tail Estimation by an Extension of the General Pareto Distribution
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.
JOOSSENS Elisabeth;
BEIRLANT Jan;
SEGERS Johan;
2006-02-16
JRC30839
EUR 21881 EN,
https://publications.jrc.ec.europa.eu/repository/handle/JRC30839,
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