IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v150y2022icp147-191.html
   My bibliography  Save this article

Tails of bivariate stochastic recurrence equation with triangular matrices

Author

Listed:
  • Damek, Ewa
  • Matsui, Muneya

Abstract

We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions W=(W1,W2). Recently it has been observed that W1,W2 may exhibit regularly varying tails with different indices, which is in contrast to well-known Kesten-type results. However, only partial results have been derived. Under typical “Kesten–Goldie” and “Grey” conditions, we completely characterize tail behavior of W1,W2. The tail asymptotics we obtain has not been observed in previous settings of stochastic recurrence equations.

Suggested Citation

  • Damek, Ewa & Matsui, Muneya, 2022. "Tails of bivariate stochastic recurrence equation with triangular matrices," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 147-191.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:147-191
    DOI: 10.1016/j.spa.2022.04.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922000898
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.04.008?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. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    3. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    4. Horváth, Roman & Šopov, Boril, 2016. "GARCH models, tail indexes and error distributions: An empirical investigation," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 1-15.
    5. Sun, Pengfei & Zhou, Chen, 2014. "Diagnosing the distribution of GARCH innovations," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 287-303.
    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. Marc S. Paolella, 2017. "The Univariate Collapsing Method for Portfolio Optimization," Econometrics, MDPI, vol. 5(2), pages 1-33, May.
    2. Fernández, Begoña & Muriel, Nelson, 2009. "Regular variation and related results for the multivariate GARCH(p,q) model with constant conditional correlations," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1538-1550, August.
    3. Boussama, Farid & Fuchs, Florian & Stelzer, Robert, 2011. "Stationarity and geometric ergodicity of BEKK multivariate GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2331-2360, October.
    4. 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.
    5. Guochang Wang & Wai Keung Li & Ke Zhu, 2018. "New HSIC-based tests for independence between two stationary multivariate time series," Papers 1804.09866, arXiv.org.
    6. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.
    7. Abu S. Amin & Lucjan T. Orlowski, 2014. "Returns, Volatilities, and Correlations Across Mature, Regional, and Frontier Markets: Evidence from South Asia," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 50(3), pages 5-27, May.
    8. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    9. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    10. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    11. Manabu Asai & Michael McAleer, 2009. "Dynamic Conditional Correlations for Asymmetric Processes," CARF F-Series CARF-F-168, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. Kyritsis, Evangelos & Serletis, Apostolos, 2018. "The zero lower bound and market spillovers: Evidence from the G7 and Norway," Research in International Business and Finance, Elsevier, vol. 44(C), pages 100-123.
    13. Chulwoo Han & Frank C. Park & Jangkoo Kang, 2017. "A geometric treatment of time-varying volatilities," Review of Quantitative Finance and Accounting, Springer, vol. 49(4), pages 1121-1141, November.
    14. Onour, Ibrahim, 2011. "Does credit for equity investments feedback on stock market volatility? Evidence from an emerging stock market," MPRA Paper 28001, University Library of Munich, Germany.
    15. Luc Bauwens & Edoardo Otranto, 2023. "Modeling Realized Covariance Matrices: A Class of Hadamard Exponential Models," Journal of Financial Econometrics, Oxford University Press, vol. 21(4), pages 1376-1401.
    16. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    17. de Goeij, Peter & Marquering, Wessel, 2009. "Stock and bond market interactions with level and asymmetry dynamics: An out-of-sample application," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 318-329, March.
    18. Mensi, Walid & Hammoudeh, Shawkat & Nguyen, Duc Khuong & Yoon, Seong-Min, 2014. "Dynamic spillovers among major energy and cereal commodity prices," Energy Economics, Elsevier, vol. 43(C), pages 225-243.
    19. Eli Bouri & Andre Eid & Imad Kachacha, 2014. "The Dynamic Behaviour and Determinants of Linkages among Middle Eastern and North African Stock Exchanges," Economic Issues Journal Articles, Economic Issues, vol. 19(1), pages 1-22, March.
    20. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.

    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:150:y:2022:i:c:p:147-191. 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.