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Which Extreme Values are Really Extremes?

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  • Jose Olmo
  • Jesus Gonzalo

Abstract

The aim of this paper is to give a formal definition and consistent estimates of the extremes of a population. This definition relies on a threshold value that delimits the extremes and on the uniform convergence of the distribution of these extremes to a Pareto type distribution. The tail parameter of this Pareto type distribution is the tail index of the data distribution. The estimator of the threshold is anchored in the Kolmogorov-Smirnov distance between consistent estimates of those two distributions. Our estimator is consistent and via the construction of confidence intervals for the tail index (derived from our threshold estimator) we overcome the bias problems of the usual tail index estimators (Hill or Pickands). The paper also explores the validity of our definition for standard sample sizes. For this purpose, a hypothesis test is designed in order to reject extremes estimates that are not really extremes. Applications for different stock returns are presented

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 144.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:144

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Related research

Keywords: Bootstrap; Goodness of fit test; Hill estimator; Kolmogorov-Smirnov distance; Balkema and De-Haan; Pickands Theorem; Tail index.;

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Cited by:
  1. Jalal, Amine & Rockinger, Michael, 2008. "Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 868-877, December.
  2. Ana-Maria Gavril, 2009. "Exchange Rate Risk: Heads or Tails," Advances in Economic and Financial Research - DOFIN Working Paper Series 35, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
  3. Koopman, Siem Jan & Shephard, Neil & Creal, Drew, 2009. "Testing the assumptions behind importance sampling," Journal of Econometrics, Elsevier, vol. 149(1), pages 2-11, April.
  4. Loriano Mancini & Fabio Trojani, 2005. "Robust Value at Risk Prediction," Swiss Finance Institute Research Paper Series 07-31, Swiss Finance Institute, revised Oct 2007.
  5. Bertrand B. Maillet & Jean-Philippe R. M├ędecin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
  6. Olmo, J., 2009. "Extreme Value Theory Filtering Techniques for Outlier Detection," Working Papers 09/09, Department of Economics, City University London.
  7. Bekiros, Stelios D. & Georgoutsos, Dimitris A., 2008. "The extreme-value dependence of Asia-Pacific equity markets," Journal of Multinational Financial Management, Elsevier, vol. 18(3), pages 197-208, July.

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