IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v28y2012i01p179-206_00.html
   My bibliography  Save this article

Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models

Author

Listed:
  • Francq, Christian
  • Zakoïan, Jean-Michel

Abstract

We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameters of a class of multivariate asymmetric generalized autoregressive conditionally heteroskedastic processes, allowing for cross leverage effects. The conditions required to establish the asymptotic properties of the QMLE are mild and coincide with the minimal ones in the univariate case. In particular, no moment assumption is made on the observed process. Instead, we require strict stationarity, for which a necessary and sufficient condition is established. The asymptotic results are illustrated by Monte Carlo experiments, and an application to a bivariate exchange rates series is proposed.

Suggested Citation

  • Francq, Christian & Zakoïan, Jean-Michel, 2012. "Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models," Econometric Theory, Cambridge University Press, vol. 28(01), pages 179-206, February.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:01:p:179-206_00
    as

    Download full text from publisher

    File URL: http://journals.cambridge.org/abstract_S0266466611000156
    File Function: link to article abstract page
    Download Restriction: no

    Citations

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


    Cited by:

    1. Francq, Christian & Jiménez Gamero, Maria Dolores & Meintanis, Simos, 2015. "Tests for sphericity in multivariate garch models," MPRA Paper 67411, University Library of Munich, Germany.
    2. Christian Francq & Lajos Horváth & Jean-Michel Zakoïan, 2016. "Variance Targeting Estimation of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(2), pages 353-382.
    3. Francq, Christian & Zakoian, Jean-Michel, 2015. "Joint inference on market and estimation risks in dynamic portfolios," MPRA Paper 68100, University Library of Munich, Germany.
    4. Wojciech Charemza & Carlos Diaz Vela & Svetlana Makarova, 2013. "Inflation fan charts, monetary policy and skew normal distribution," Discussion Papers in Economics 13/06, Department of Economics, University of Leicester.
    5. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    6. Wintenberger, Olivier & Cai, Sixiang, 2011. "Parametric inference and forecasting in continuously invertible volatility models," MPRA Paper 31767, University Library of Munich, Germany.
    7. Conrad, Christian & Weber, Enzo, 2013. "Measuring Persistence in Volatility Spillovers," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79850, Verein für Socialpolitik / German Economic Association.
    8. Christian Francq & Jean-Michel Zakoïan, 2016. "Estimating multivariate volatility models equation by equation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 613-635, June.
    9. Francq, Christian & Zakoian, Jean-Michel, 2014. "Estimating multivariate GARCH and stochastic correlation models equation by equation," MPRA Paper 54250, University Library of Munich, Germany.
    10. repec:eee:intfor:v:34:y:2018:i:1:p:45-63 is not listed on IDEAS
    11. Francq, C. & Jiménez-Gamero, M.D. & Meintanis, S.G., 2017. "Tests for conditional ellipticity in multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 196(2), pages 305-319.
    12. Darolles, Serges & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," MPRA Paper 83988, University Library of Munich, Germany.
    13. Santos, André A.P. & Moura, Guilherme V., 2014. "Dynamic factor multivariate GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 606-617.
    14. Conrad, Christian & Loch, Karin & Rittler, Daniel, 2014. "On the macroeconomic determinants of long-term volatilities and correlations in U.S. stock and crude oil markets," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 26-40.
    15. Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.
    16. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.

    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:cup:etheor:v:28:y:2012:i:01:p:179-206_00. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters). General contact details of provider: http://journals.cambridge.org/jid_ECT .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.