IDEAS home Printed from https://ideas.repec.org/p/cir/cirwor/2004s-31.html
   My bibliography  Save this paper

Estimation de densité conditionnelle lorsque l'hypothèse de normalité est insatisfaisante

Author

Listed:
  • Julie Carreau
  • Yoshua Bengio

Abstract

We aim at modelling fat-tailed densities whose distributions are unknown but are potentially asymmetric. In this context, the standard normality assumption is not appropriate.In order to make as few distributional assumptions as possible, we use a non-parametric algorithm to model the center of the distribution. Density modelling becomes more difficult as we move further in the tail of the distribution since very few observations fall in the upper tail area. Hence we decide to use the generalized Pareto distribution (GPD) to model the tails of the distribution. The GPD can approximate finite, exponential or subexponential tails. The estimation of the parameters of the GPD is based solely on the extreme observations. An observation is defined as being extreme if it is greater than a given threshold. The main difficulty with GPD modelling is to determine an appropriate threshold. Nous cherchons à modéliser des densités dont la distribution est inconnue mais qui est asymétrique et présente des queues lourdes. Dans ce contexte, l'hypothèse de normalité n'est pas appropriée. Afin de maintenir au minimum le nombre d'hypothèses distributionnelles, nous utilisons une méthode non paramétrique pour modéliser le centre de la distribution. La modélisation est plus difficile dans les queues de la distribution puisque peu d'observations s'y trouvent. Nous nous proposons donc d'utiliser la Pareto généralisée (GPD) pour modéliser les queues de la distribution. La GPD permet d'approximer tous les types de queues de distributions (qu'elles soient finies, exponentielles ou sous-exponentielles). L'estimation des paramètres de la GPD est uniquement basée sur les observations extrêmes. Une observation est définie comme étant extrême si elle dépasse un seuil donné. La principale difficulté de la modélisation avec la GPD réside dans le choix d'un seuil adéquat.

Suggested Citation

  • Julie Carreau & Yoshua Bengio, 2004. "Estimation de densité conditionnelle lorsque l'hypothèse de normalité est insatisfaisante," CIRANO Working Papers 2004s-31, CIRANO.
    • Handle: RePEc:cir:cirwor:2004s-31
    as

    Download full text from publisher

    File URL: https://cirano.qc.ca/files/publications/2004s-31.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Phillipe Lambert & J. K. Lindsey, 1999. "Analysing Financial Returns by Using Regression Models Based on Non‐Symmetric Stable Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 409-424.
    2. Beirlant, Jan & Goegebeur, Yuri, 2003. "Regression with response distributions of Pareto-type," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 595-619, April.
    3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C.P., 2005. "An evaluation framework for alternative VaR-models," Journal of International Money and Finance, Elsevier, vol. 24(6), pages 944-958, October.
    2. Lehnert, Thorsten & Wolff, Christian C. P., 2004. "Scale-consistent Value-at-Risk," Finance Research Letters, Elsevier, vol. 1(2), pages 127-134, June.
    3. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    4. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    5. Ibrahim Ergen, 2014. "Tail dependence and diversification benefits in emerging market stocks: an extreme value theory approach," Applied Economics, Taylor & Francis Journals, vol. 46(19), pages 2215-2227, July.
    6. Gonzalo Cortazar & Alejandro Bernales & Diether Beuermann, 2005. "Methodology and Implementation of Value-at-Risk Measures in Emerging Fixed-Income Markets with Infrequent Trading," Finance 0512030, University Library of Munich, Germany.
    7. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    8. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    9. Balla, Eliana & Ergen, Ibrahim & Migueis, Marco, 2014. "Tail dependence and indicators of systemic risk for large US depositories," Journal of Financial Stability, Elsevier, vol. 15(C), pages 195-209.
    10. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    11. Carol Alexander & Emese Lazar & Silvia Stanescu, 2011. "Analytic Approximations to GARCH Aggregated Returns Distributions with Applications to VaR and ETL," ICMA Centre Discussion Papers in Finance icma-dp2011-08, Henley Business School, University of Reading.
    12. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.
    13. George Kouretas & Leonidas Zarangas, 2005. "Conditional autoregressive valu at risk by regression quantile: Estimatingmarket risk for major stock markets," Working Papers 0521, University of Crete, Department of Economics.
    14. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 75, European Central Bank.
    15. Nicolau, João & Rodrigues, Paulo M.M. & Stoykov, Marian Z., 2023. "Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics," Journal of Econometrics, Elsevier, vol. 235(2), pages 2266-2284.
    16. Wagner, Niklas, 2005. "Autoregressive conditional tail behavior and results on Government bond yield spreads," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 247-261.
    17. Hassan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi, 2016. "Elliptical tempered stable distribution," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1069-1087, July.
    18. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    19. Gordon V. Chavez, 2019. "Dynamic tail inference with log-Laplace volatility," Papers 1901.02419, arXiv.org, revised Jul 2019.
    20. Med Imen Gallali & Raggad Zahraa, 2012. "Evaluation of VaR models' forecasting performance: the case of oil markets," International Journal of Financial Services Management, Inderscience Enterprises Ltd, vol. 5(3), pages 197-215.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2004s-31. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Webmaster (email available below). General contact details of provider: https://edirc.repec.org/data/ciranca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.