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Towards estimating extremal serial dependence via the bootstrapped extremogram

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  • Davis, Richard A.
  • Mikosch, Thomas
  • Cribben, Ivor

Abstract

Davis and Mikosch (2009a) introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram. A major difficulty was the construction of credible confidence bands for the extremogram. In this paper, we employ the stationary bootstrap to overcome this problem. The use of the stationary bootstrap for the extremogram and the resulting interpretations are illustrated with several financial time series.

Suggested Citation

  • Davis, Richard A. & Mikosch, Thomas & Cribben, Ivor, 2012. "Towards estimating extremal serial dependence via the bootstrapped extremogram," Journal of Econometrics, Elsevier, vol. 170(1), pages 142-152.
    • Handle: RePEc:eee:econom:v:170:y:2012:i:1:p:142-152
    DOI: 10.1016/j.jeconom.2012.04.003
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    1. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
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    Cited by:

    1. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2017. "Extreme M-quantiles as risk measures: From L1 to Lp optimization," TSE Working Papers 17-841, Toulouse School of Economics (TSE).
    2. Vanem, Erik, 2023. "Analysing multivariate extreme conditions using environmental contours and accounting for serial dependence," Renewable Energy, Elsevier, vol. 202(C), pages 470-482.
    3. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    4. Herrera, R. & Clements, A.E., 2018. "Point process models for extreme returns: Harnessing implied volatility," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 161-175.
    5. Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    6. Lehtomaa, Jaakko & Resnick, Sidney I., 2020. "Asymptotic independence and support detection techniques for heavy-tailed multivariate data," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 262-277.
    7. Davis, Richard & Drees, Holger & Segers, Johan & Warchol, Michal, 2018. "Inference on the tail process with application to financial time series modelling," LIDAM Discussion Papers ISBA 2018002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Nikolaus Hautsch & Rodrigo Herrera, 2020. "Multivariate dynamic intensity peaks‐over‐threshold models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 248-272, March.
    9. Aviral Kumar Tiwari & Muhammad Shahbaz & Rabeh Khalfaoui & Rizwan Ahmed & Shawkat Hammoudeh, 2024. "Directional predictability from energy markets to exchange rates and stock markets in the emerging market countries (E7 + 1): New evidence from cross‐quantilogram approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 719-789, January.
    10. Damek, Ewa & Mikosch, Thomas & Zhao, Yuwei & Zienkiewicz, Jacek, 2023. "Whittle estimation based on the extremal spectral density of a heavy-tailed random field," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 232-267.
    11. Lin Han & Ivor Cribben & Stefan Trueck, 2022. "Extremal Dependence in Australian Electricity Markets," Papers 2202.09970, arXiv.org.
    12. Davis, Richard & Holger, Drees & Segers, Johan & Warchol, Michal, 2016. "Modeling serial extremal dependence," LIDAM Discussion Papers ISBA 2016016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Richard A. Davis & Claudia Klüppelberg & Christina Steinkohl, 2013. "Statistical inference for max-stable processes in space and time," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 791-819, November.
    14. Mikosch, Thomas & Zhao, Yuwei, 2015. "The integrated periodogram of a dependent extremal event sequence," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3126-3169.
    15. Todorova, Neda, 2017. "The intraday directional predictability of large Australian stocks: A cross-quantilogram analysis," Economic Modelling, Elsevier, vol. 64(C), pages 221-230.
    16. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    17. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    18. Duan, Kun & Ren, Xiaohang & Wen, Fenghua & Chen, Jinyu, 2023. "Evolution of the information transmission between Chinese and international oil markets: A quantile-based framework," Journal of Commodity Markets, Elsevier, vol. 29(C).
    19. Fuentes, Fernanda & Herrera, Rodrigo & Clements, Adam, 2023. "Forecasting extreme financial risk: A score-driven approach," International Journal of Forecasting, Elsevier, vol. 39(2), pages 720-735.
    20. Yong Bum Cho & Richard A. Davis & Souvik Ghosh, 2016. "Asymptotic Properties of the Empirical Spatial Extremogram," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 757-773, September.

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    More about this item

    Keywords

    Extremogram; Extremal dependence; Stationary bootstrap; Financial time series;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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