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Tail index estimation: quantile driven threshold selection

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  • Danielsson, Jon
  • Ergun, Lerby M.
  • Haan, Laurens de
  • Vries, Casper G. de

Abstract

The selection of upper order statistics in tail estimation is notoriously difficult. Most methods are based on asymptotic arguments, like minimizing the asymptotic mse, that do not perform well in finite samples. Here we advance a data driven method that minimizes the maximum distance between the fitted Pareto type tail and the observed quantile. To analyse the finite sample properties of the metric we organize a horse race between the other methods. In most cases the finite sample based methods perform best. To demonstrate the economic relevance of choosing the proper methodology we use daily equity return data from the CRSP database and find economic relevant variation between the tail index estimates.

Suggested Citation

  • Danielsson, Jon & Ergun, Lerby M. & Haan, Laurens de & Vries, Casper G. de, 2016. "Tail index estimation: quantile driven threshold selection," LSE Research Online Documents on Economics 66193, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:66193
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    Cited by:

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    3. Tjeerd de Vries & Alexis Akira Toda, 2022. "Capital and Labor Income Pareto Exponents Across Time and Space," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(4), pages 1058-1078, December.
    4. Matthias Schnaubelt & Jonas Rende & Christopher Krauss, 2019. "Testing Stylized Facts of Bitcoin Limit Order Books," JRFM, MDPI, vol. 12(1), pages 1-30, February.
    5. Krzysztof Echaust & Małgorzata Just, 2021. "Tail Dependence between Crude Oil Volatility Index and WTI Oil Price Movements during the COVID-19 Pandemic," Energies, MDPI, vol. 14(14), pages 1-21, July.
    6. Echaust, Krzysztof & Just, Małgorzata & Kliber, Agata, 2024. "To hedge or not to hedge? Cryptocurrencies, gold and oil against stock market risk," International Review of Financial Analysis, Elsevier, vol. 94(C).
    7. Jon Danielsson & Lerby Ergun & Casper G. de Vries, 2018. "Challenges in Implementing Worst-Case Analysis," Staff Working Papers 18-47, Bank of Canada.
    8. Hoga, Yannick, 2021. "The uncertainty in extreme risk forecasts from covariate-augmented volatility models," International Journal of Forecasting, Elsevier, vol. 37(2), pages 675-686.
    9. Lerby Ergun, 2019. "Extreme Downside Risk in Asset Returns," Staff Working Papers 19-46, Bank of Canada.
    10. Natalia Markovich & Maksim Ryzhov & Marijus Vaičiulis, 2022. "Tail Index Estimation of PageRanks in Evolving Random Graphs," Mathematics, MDPI, vol. 10(16), pages 1-26, August.
    11. Echaust, Krzysztof, 2021. "Asymmetric tail dependence between stock market returns and implied volatility," The Journal of Economic Asymmetries, Elsevier, vol. 23(C).
    12. Ergun, Lerby M., 2016. "Disaster and fortune risk in asset returns," LSE Research Online Documents on Economics 66194, London School of Economics and Political Science, LSE Library.

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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