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Tail Index Estimation: Quantile-Driven Threshold Selection

Author

Listed:
  • Jon Danielsson
  • Lerby Ergun
  • Laurens de Haan
  • Casper G. de Vries

Abstract

The selection of upper order statistics in tail estimation is notoriously difficult. Methods that are based on asymptotic arguments, like minimizing the asymptotic MSE, 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 analyze the finite sample properties of the metric, we perform rigorous simulation studies. 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 economically relevant variation between the tail index estimates.

Suggested Citation

  • Jon Danielsson & Lerby Ergun & Laurens de Haan & Casper G. de Vries, 2019. "Tail Index Estimation: Quantile-Driven Threshold Selection," Staff Working Papers 19-28, Bank of Canada.
    • Handle: RePEc:bca:bocawp:19-28
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    References listed on IDEAS

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    Cited by:

    1. Matthias Schnaubelt & Jonas Rende & Christopher Krauss, 2019. "Testing Stylized Facts of Bitcoin Limit Order Books," JRFM, MDPI, vol. 12(1), pages 1-30, February.
    2. Jon Danielsson & Lerby Ergun & Casper G. de Vries, 2018. "Challenges in Implementing Worst-Case Analysis," Staff Working Papers 18-47, Bank of Canada.
    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. Echaust, Krzysztof, 2021. "Asymmetric tail dependence between stock market returns and implied volatility," The Journal of Economic Asymmetries, Elsevier, vol. 23(C).
    5. Lerby Ergun, 2019. "Extreme Downside Risk in Asset Returns," Staff Working Papers 19-46, Bank of Canada.
    6. 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.
    7. Krzysztof Echaust & Małgorzata Just, 2020. "Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    8. Małgorzata Just & Krzysztof Echaust, 2021. "An Optimal Tail Selection in Risk Measurement," Risks, MDPI, vol. 9(4), pages 1-16, April.
    9. 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.
    10. 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.
    11. 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).
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    More about this item

    Keywords

    Econometric and statistical methods; Financial stability;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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