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

Author

Listed:
  • Nehla, Debbabi

    (SUP'COM - Ecole Supérieure des Communications de Tunis)

  • Marie, Kratz

    (Essec Business School)

  • Mamadou , Mboup

    (CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication)

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.

Suggested Citation

  • Nehla, Debbabi & Marie, Kratz & Mamadou , Mboup, 2016. "A self-calibrating method for heavy tailed data modeling : Application in neuroscience and finance," ESSEC Working Papers WP1619, ESSEC Research Center, ESSEC Business School.
    • Handle: RePEc:ebg:essewp:dr-16019
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    File URL: https://hal-essec.archives-ouvertes.fr/hal-01424298/document
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    References listed on IDEAS

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    2. Dacorogna, Michel & Kratz, Marie, 2015. "Living in a Stochastic World and Managing Complex Risks," ESSEC Working Papers WP1517, ESSEC Research Center, ESSEC Business School.
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    4. Dacorogna, Michel & Kratz, Marie, 2015. "Living in a Stochastic World and Managing Complex Risks," ESSEC Working Papers WP1517, ESSEC Research Center, ESSEC Business School.
    5. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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    More about this item

    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;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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