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Diagnostics for dependence within time series extremes

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  • Anthony W. Ledford
  • Jonathan A. Tawn

Abstract

Summary. The analysis of extreme values within a stationary time series entails various assumptions concerning its long‐ and short‐range dependence. We present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events. These tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and identically distributed variables. Our diagnostic aids are illustrated through theoretical examples, simulation studies and by application to rainfall and exchange rate data. On the basis of these diagnostics we can explain characteristics that are found in the observed extreme events of these series and also gain insight into the properties of events that are more extreme than those observed.

Suggested Citation

  • Anthony W. Ledford & Jonathan A. Tawn, 2003. "Diagnostics for dependence within time series extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 521-543, May.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:2:p:521-543
    DOI: 10.1111/1467-9868.00400
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    Cited by:

    1. Pushpa Dissanayake & Teresa Flock & Johanna Meier & Philipp Sibbertsen, 2021. "Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights," Mathematics, MDPI, vol. 9(21), pages 1-33, November.
    2. Ferreira, Helena & Ferreira, Marta, 2012. "Tail dependence between order statistics," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 176-192.
    3. James, Robert & Leung, Henry & Leung, Jessica Wai Yin & Prokhorov, Artem, 2023. "Forecasting tail risk measures for financial time series: An extreme value approach with covariates," Journal of Empirical Finance, Elsevier, vol. 71(C), pages 29-50.
    4. Stan Tendijck & Philip Jonathan & David Randell & Jonathan Tawn, 2024. "Temporal evolution of the extreme excursions of multivariate k$$ k $$th order Markov processes with application to oceanographic data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    5. Cooley, Daniel & Davis, Richard A. & Naveau, Philippe, 2010. "The pairwise beta distribution: A flexible parametric multivariate model for extremes," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2103-2117, October.
    6. Kim, Mihyun & Kokoszka, Piotr, 2022. "Extremal dependence measure for functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    8. Aknouche, Abdelhakim & Scotto, Manuel, 2022. "A multiplicative thinning-based integer-valued GARCH model," MPRA Paper 112475, University Library of Munich, Germany.
    9. Zhang, Zhengjun & Shinki, Kazuhiko, 2007. "Extreme co-movements and extreme impacts in high frequency data in finance," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1399-1415, May.
    10. Fan Yang & Yi Zhang, 2024. "Asymptotics of Sum of Heavy-tailed Risks with Copulas," Papers 2411.09657, arXiv.org.
    11. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    12. de Haan, Laurens & Neves, Cláudia & Peng, Liang, 2008. "Parametric tail copula estimation and model testing," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1260-1275, July.
    13. Ceylan Onay & Gözde Ünal, 2012. "Cointegration and Extreme Value Analyses of Bovespa and the Istanbul Stock Exchange," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(1), pages 66-90, February.
    14. Zhang, Zhengjun & Zhu, Bin, 2016. "Copula structured M4 processes with application to high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 231-241.
    15. Zhang, Zhengjun & Huang, James, 2006. "Extremal financial risk models and portfolio evaluation," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2313-2338, December.
    16. John G. Galbraith & Serguei Zernov, 2006. "Extreme Dependence In The Nasdaq And S&P Composite Indexes," Departmental Working Papers 2006-14, McGill University, Department of Economics.

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