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Which Extreme Values Are Really Extreme?

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  • Jesus Gonzalo

Abstract

We define the extreme values of any random sample of size n from a distribution function F as the observations exceeding a threshold and following a type of generalized Pareto distribution (GPD) involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD. To formalize the definition we use a semiparametric bootstrap to test the corresponding GPD approximation. Finally, we use our methodology to estimate the tail index and value at risk (VaR) of some financial indexes of major stock markets. Copyright 2004, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 2 (2004)
Issue (Month): 3 ()
Pages: 349-369

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Handle: RePEc:oup:jfinec:v:2:y:2004:i:3:p:349-369

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Cited by:
  1. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2013. "Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management, Springer, Springer, vol. 27(7), pages 2325-2352, May.
  2. Bekiros, Stelios D. & Georgoutsos, Dimitris A., 2008. "The extreme-value dependence of Asia-Pacific equity markets," Journal of Multinational Financial Management, Elsevier, Elsevier, vol. 18(3), pages 197-208, July.
  3. Loriano Mancini & Fabio Trojani, 2007. "Robust Value at Risk Prediction," University of St. Gallen Department of Economics working paper series 2007, Department of Economics, University of St. Gallen 2007-36, Department of Economics, University of St. Gallen.
  4. Ana-Maria Gavril, 2009. "Exchange Rate Risk: Heads or Tails," Advances in Economic and Financial Research - DOFIN Working Paper Series, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB 35, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
  5. 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, Elsevier, vol. 15(5), pages 868-877, December.
  6. Bertrand B. Maillet & Jean-Philippe R. Médecin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers, Department of Economics, University of Venice "Ca' Foscari" 2010_10, Department of Economics, University of Venice "Ca' Foscari".
  7. Koopman, Siem Jan & Shephard, Neil & Creal, Drew, 2009. "Testing the assumptions behind importance sampling," Journal of Econometrics, Elsevier, Elsevier, vol. 149(1), pages 2-11, April.
  8. Olmo, J., 2009. "Extreme Value Theory Filtering Techniques for Outlier Detection," Working Papers, Department of Economics, City University London 09/09, Department of Economics, City University London.
  9. Schluter, Christian & Trede, Mark, 2008. "Identifying multiple outliers in heavy-tailed distributions with an application to market crashes," Journal of Empirical Finance, Elsevier, Elsevier, vol. 15(4), pages 700-713, September.
  10. Charles, Amélie & Darné, Olivier, 2014. "Large shocks in the volatility of the Dow Jones Industrial Average index: 1928–2013," Journal of Banking & Finance, Elsevier, Elsevier, vol. 43(C), pages 188-199.

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