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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

Suggested Citation

  • Jose Olmo & Jesus Gonzalo, 2004. "Which Extreme Values are Really Extremes?," Econometric Society 2004 North American Winter Meetings 144, Econometric Society.
  • Handle: RePEc:ecm:nawm04:144
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    Cited by:

    1. Schluter, Christian & Trede, Mark, 2008. "Identifying multiple outliers in heavy-tailed distributions with an application to market crashes," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 700-713, September.
    2. 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.
    3. 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.
    4. Charles, Amélie & Darné, Olivier, 2014. "Large shocks in the volatility of the Dow Jones Industrial Average index: 1928–2013," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 188-199.
    5. Nikola Radivojevic & Milena Cvjetkovic & Saša Stepanov, 2016. "The new hybrid value at risk approach based on the extreme value theory," Estudios de Economia, University of Chile, Department of Economics, vol. 43(1 Year 20), pages 29-52, June.
    6. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.
    7. Loriano Mancini & Fabio Trojani, 2011. "Robust Value at Risk Prediction," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 281-313, Spring.
    8. Olmo, J., 2009. "Extreme Value Theory Filtering Techniques for Outlier Detection," Working Papers 09/09, Department of Economics, City University London.
    9. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    10. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    11. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2013. "Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2325-2352, May.
    12. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    13. 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.
    14. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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