IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i8p3126-3169.html
   My bibliography  Save this article

The integrated periodogram of a dependent extremal event sequence

Author

Listed:
  • Mikosch, Thomas
  • Zhao, Yuwei

Abstract

We investigate the asymptotic properties of the integrated periodogram calculated from a sequence of indicator functions of dependent extremal events. An event in Euclidean space is extreme if it occurs far away from the origin. We use a regular variation condition on the underlying stationary sequence to make these notions precise. Our main result is a functional central limit theorem for the integrated periodogram of the indicator functions of dependent extremal events. The limiting process is a continuous Gaussian process whose covariance structure is in general unfamiliar, but in the i.i.d. case a Brownian bridge appears. In the general case, we propose a stationary bootstrap procedure for approximating the distribution of the limiting process. The developed theory can be used to construct classical goodness-of-fit tests such as the Grenander–Rosenblatt and Cramér–von Mises tests which are based only on the extremes in the sample. We apply the test statistics to simulated and real-life data.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:3126-3169
    DOI: 10.1016/j.spa.2015.02.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915000678
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2015.02.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dahlhaus, Rainer, 1988. "Empirical spectral processes and their applications to time series analysis," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 69-83, November.
    2. Dehling, Herold & Durieu, Olivier & Volny, Dalibor, 2009. "New techniques for empirical processes of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3699-3718, October.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jozef Baruník & Tobias Kley, 2019. "Quantile coherency: A general measure for dependence between cyclical economic variables," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 131-152.
    2. 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.
    3. Sourav Das & Suhasini Subba Rao & Junho Yang, 2021. "Spectral methods for small sample time series: A complete periodogram approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 597-621, September.
    4. Lin Han & Ivor Cribben & Stefan Trueck, 2022. "Extremal Dependence in Australian Electricity Markets," Papers 2202.09970, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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).
    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. Todorova, Neda, 2017. "The intraday directional predictability of large Australian stocks: A cross-quantilogram analysis," Economic Modelling, Elsevier, vol. 64(C), pages 221-230.
    5. 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).
    6. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    7. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    8. Lin Han & Ivor Cribben & Stefan Trueck, 2022. "Extremal Dependence in Australian Electricity Markets," Papers 2202.09970, arXiv.org.
    9. Wang, Yizao, 2014. "Convergence to the maximum process of a fractional Brownian motion with shot noise," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 33-41.
    10. Fasen-Hartmann, Vicky & Mayer, Celeste, 2023. "Empirical spectral processes for stationary state space models," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 319-354.
    11. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    12. Axel Bücher & Holger Dette & Florian Heinrichs, 2020. "Detecting deviations from second-order stationarity in locally stationary functional time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1055-1094, August.
    13. Raphaël de Fondeville & Anthony C. Davison, 2022. "Functional peaks‐over‐threshold analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1392-1422, September.
    14. Philip Preuss & Ruprecht Puchstein & Holger Dette, 2015. "Detection of Multiple Structural Breaks in Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 654-668, June.
    15. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    16. Barrera, David & Peligrad, Costel & Peligrad, Magda, 2016. "On the functional CLT for stationary Markov chains started at a point," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 1885-1900.
    17. 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.
    18. Segers, Johan & Zhao, Yuwei & Meinguet, Thomas, 2016. "Radial-angular decomposition of regularly varying time series in star-shaped metric spaces," LIDAM Discussion Papers ISBA 2016017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Mikosch, T. & Norvaisa, R., 1997. "Uniform convergence of the empirical spectral distribution function," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 85-114, October.
    20. Ruprecht Puchstein & Philip Preuß, 2016. "Testing for Stationarity in Multivariate Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 3-29, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:3126-3169. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.