IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v43y2022i5p750-780.html
   My bibliography  Save this article

Asymptotic independence ex machina: Extreme value theory for the diagonal SRE model

Author

Listed:
  • Sebastian Mentemeier
  • Olivier Wintenberger

Abstract

We consider multivariate stationary processes (Xt) satisfying a stochastic recurrence equation of the form Xt=𝕄tXt−1+Qt, where (Qt) are i.i.d. random vectors and 𝕄t=Diag(b1+c1Mt,…,bd+cdMt) are i.i.d. diagonal matrices and (Mt) are i.i.d. random variables. We obtain a full characterization of the vector scaling regular variation properties of (Xt), proving that some coordinates Xt, i and Xt, j are asymptotically independent even though all coordinates rely on the same random input (Mt). We prove the asynchrony of extreme clusters among marginals with different tail indices. Our results are applied to some multivariate autoregressive conditional heteroskedastic (BEKK‐ARCH and CCC‐GARCH) processes and to log‐returns. Angular measure inference shows evidences of asymptotic independence among marginals of diagonal SRE with different tail indices.

Suggested Citation

  • Sebastian Mentemeier & Olivier Wintenberger, 2022. "Asymptotic independence ex machina: Extreme value theory for the diagonal SRE model," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 750-780, September.
    • Handle: RePEc:bla:jtsera:v:43:y:2022:i:5:p:750-780
    DOI: 10.1111/jtsa.12637
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12637
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12637?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
    ---><---

    References listed on IDEAS

    as
    1. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    2. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    3. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    4. Buraczewski, D. & Damek, E. & Zienkiewicz, J., 2018. "Pointwise estimates for first passage times of perpetuity sequences," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2923-2951.
    Full references (including those not matched with items on IDEAS)

    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. Jumah, Adusei & Kunst, Robert M., 2001. "The Effects of Exchange-Rate Exposures on Equity Asset Markets," Economics Series 94, Institute for Advanced Studies.
    2. Pedersen, Rasmus Søndergaard, 2016. "Targeting Estimation Of Ccc-Garch Models With Infinite Fourth Moments," Econometric Theory, Cambridge University Press, vol. 32(2), pages 498-531, April.
    3. Lanza, Alessandro & Manera, Matteo & McAleer, Michael, 2006. "Modeling dynamic conditional correlations in WTI oil forward and futures returns," Finance Research Letters, Elsevier, vol. 3(2), pages 114-132, June.
    4. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    5. Monica Billio & Maddalena Cavicchioli, 2013. "�Markov Switching Models for Volatility: Filtering, Approximation and Duality�," Working Papers 2013:24, Department of Economics, University of Venice "Ca' Foscari".
    6. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
    7. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modĂŠles ARCH en finance : un point sur la thĂŠorie et les rĂŠsultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    8. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," UniversitĂŠ Paris1 PanthĂŠon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    9. Hoti, Suhejla, 2005. "Comparative analysis of risk ratings for the East European region," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 449-462.
    10. Hu, Michael Y. & Tsoukalas, Christos, 1999. "Combining conditional volatility forecasts using neural networks: an application to the EMS exchange rates," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 9(4), pages 407-422, November.
    11. Suhejla Hoti & Felix Chan & Michael McAleer, 2003. "Structure and Asymptotic Theory for Multivariate Asymmetric Volatility: Empirical Evidence for Country Risk Ratings," CIRJE F-Series CIRJE-F-203, CIRJE, Faculty of Economics, University of Tokyo.
    12. Sondre Hølleland & Hans Arnfinn Karlsen, 2020. "A Stationary Spatio‐Temporal GARCH Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 177-209, March.
    13. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    14. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
    15. Mohini GUPTA & Purwa SRIVASTAVA & Amritkant MISHRA & Malayaranjan SAHOO, 2021. "Time-varying volatility spillover of foreign exchange rate in three Asian markets: Based on DCC-GARCH approach," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(629), W), pages 105-120, Winter.
    16. Suhejla Hoti & Esfandiar Maasoumi & Michael McAleer & Daniel Slottje, 2009. "Measuring the Volatility in U.S. Treasury Benchmarks and Debt Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(6), pages 522-554.
    17. Odunayo Magret Olarewaju & Timilehin John Olasehinde, 2017. "Naira-Dollar Exchange Rate Volatility Modeling Using Quadratic Moving Average Conditional Heteroscedasticity (QMACH)," EuroEconomica, Danubius University of Galati, issue 2(36), pages 106-116, November.
    18. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    19. Mario Jovanovic, 2009. "Serbian foreign exchange market during 2004-2008," SEEMHN papers 19, National Bank of Serbia.
    20. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jtsera:v:43:y:2022:i:5:p:750-780. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.