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Modeling Extreme Events: Time-Varying Extreme Tail Shape

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  • Enzo D’Innocenzo
  • André Lucas
  • Bernd Schwaab
  • Xin Zhang

Abstract

We propose a dynamic semiparametric framework to study time variation in tail parameters. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail parameters. We establish parameter regions for stationarity and ergodicity and for the existence of (unconditional) moments and consider conditions for consistency and asymptotic normality of the maximum likelihood estimator for the deterministic parameters in the model. Two empirical datasets illustrate the usefulness of the approach: daily U.S. equity returns, and 15-min euro area sovereign bond yield changes.

Suggested Citation

  • Enzo D’Innocenzo & André Lucas & Bernd Schwaab & Xin Zhang, 2024. "Modeling Extreme Events: Time-Varying Extreme Tail Shape," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 903-917, July.
  • Handle: RePEc:taf:jnlbes:v:42:y:2024:i:3:p:903-917
    DOI: 10.1080/07350015.2023.2260439
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    References listed on IDEAS

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    1. F. Blasques & S. J. Koopman & A. Lucas, 2015. "Information-theoretic optimality of observation-driven time series models for continuous responses," Biometrika, Biometrika Trust, vol. 102(2), pages 325-343.
    2. Boswijk, H. Peter & Cavaliere, Giuseppe & Georgiev, Iliyan & Rahbek, Anders, 2021. "Bootstrapping non-stationary stochastic volatility," Journal of Econometrics, Elsevier, vol. 224(1), pages 161-180.
    3. Jensen, Søren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1203-1226, December.
    4. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-216, April.
    5. Blasques, Francisco & Koopman, Siem Jan & Łasak, Katarzyna & Lucas, André, 2016. "In-sample confidence bands and out-of-sample forecast bands for time-varying parameters in observation-driven models," International Journal of Forecasting, Elsevier, vol. 32(3), pages 875-887.
    6. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
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    Cited by:

    1. Eric A. Beutner & Yicong Lin & Andre Lucas, 2023. "Consistency, distributional convergence, and optimality of score-driven filters," Tinbergen Institute Discussion Papers 23-051/III, Tinbergen Institute.
    2. D’Innocenzo, Enzo & Lucas, Andre, 2024. "Dynamic partial correlation models," Journal of Econometrics, Elsevier, vol. 241(2).
    3. Enzo D'Innocenzo & Andre Lucas & Bernd Schwaab & Xin Zhang, 2024. "Joint extreme Value-at-Risk and Expected Shortfall dynamics with a single integrated tail shape parameter," Tinbergen Institute Discussion Papers 24-069/III, Tinbergen Institute.
    4. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    5. Julien Hambuckers & Li Sun & Luca Trapin, 2023. "Measuring tail risk at high-frequency: An $L_1$-regularized extreme value regression approach with unit-root predictors," Papers 2301.01362, arXiv.org.

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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