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A self-calibrating method for heavy tailed data modeling : Application in neuroscience and finance

Author

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  • Nehla Debbabi

    (SUP'COM [TUNIS] - Ecole supérieure des communications de Tunis, ESPRIT - Ecole Supérieure Privée d'Ingénierie et de Technologies)

  • Marie Kratz

    (ESSEC Business School)

  • Mamadou Mboup

    (CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 - URCA - Université de Reims Champagne-Ardenne)

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 tted. Approaches to this estimation may be classi 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 eff ectiveness 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.

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  • Nehla Debbabi & Marie Kratz & Mamadou Mboup, 2016. "A self-calibrating method for heavy tailed data modeling : Application in neuroscience and finance," Working Papers hal-01424298, HAL.
    • Handle: RePEc:hal:wpaper:hal-01424298
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01424298
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    References listed on IDEAS

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