ESSEC Working Papers,
ESSEC Research Center, ESSEC Business School

Abstract: One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fi tted. Approaches to this estimation may be classfii ed into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fi t on simulated data. Then, it is applied to real data from neuroscience and fi nance, respectively. A comparison with other more standard extreme approaches follows.

Keywords: Algorithm; Extreme Value Theory; Gaussian distribution; Generalized Pareto Distribution; Heavy tailed data; Hybrid model; Least squares optimization; Levenberg Marquardt algorithm; Neural data; S&P 500 index

JEL-codes: C02

26 pages, December 12, 2016

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