IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v23y2007i02p251-280_07.html
   My bibliography  Save this article

Semiparametric Multivariate Volatility Models

Author

Listed:
  • Hafner, Christian M.
  • Rombouts, Jeroen V.K.

Abstract

Estimation of multivariate volatility models is usually carried out by quasi maximum likelihood (QMLE), for which consistency and asymptotic normality have been proven under quite general conditions. However, there may be a substantial efficiency loss of QMLE if the true innovation distribution is not multinormal. We suggest a nonparametric estimation of the multivariate innovation distribution, based on consistent parameter estimates obtained by QMLE. We show that under standard regularity conditions the semiparametric efficiency bound can be attained. Without reparametrizing the conditional covariance matrix (which depends on the particular model used), adaptive estimation is not possible. However, in some cases the e?ciency loss of semiparametric estimation with respect to full information maximum likelihood decreases as the dimension increases. In practice, one would like to restrict the class of possible density functions to avoid the curse of dimensionality. One way of doing so is to impose the constraint that the density belongs to the class of spherical distributions, for which we also derive the semiparametric efficiency bound and an estimator that attains this bound. A simulation experiment demonstrates the e?ciency gain of the proposed estimator compared with QMLE.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(02), pages 251-280, April.
  • Handle: RePEc:cup:etheor:v:23:y:2007:i:02:p:251-280_07
    as

    Download full text from publisher

    File URL: http://journals.cambridge.org/abstract_S0266466607070119
    File Function: link to article abstract page
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    2. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639.
    3. Hodgson, Douglas J & Vorkink, Keith P, 2003. "Efficient Estimation of Conditional Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 269-283, April.
    4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    5. HAFNER, Christian & HERWARTZ, Helmut, 1998. "Volatility impulse response functions for multivariate GARCH models," CORE Discussion Papers 1998047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
    7. Gonzalez-Rivera, Gloria & Drost, Feike C., 1999. "Efficiency comparisons of maximum-likelihood-based estimators in GARCH models," Journal of Econometrics, Elsevier, vol. 93(1), pages 93-111, November.
    8. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    9. Gloria Gonzalez-Rivera, 1997. "A note on adaptation in garch models," Econometric Reviews, Taylor & Francis Journals, vol. 16(1), pages 55-68.
    10. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
    11. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    12. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
    13. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
    14. Steigerwald, Douglas G., 1992. "Adaptive estimation in time series regression models," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 251-275.
    15. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    16. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    17. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    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. 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. Fiorentini, Gabriele & Sentana, Enrique, 2018. "Consistent non-Gaussian pseudo maximum likelihood estimators," CEPR Discussion Papers 12682, C.E.P.R. Discussion Papers.
    3. Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, vol. 176(1), pages 3-17.
    4. Gouriéroux, Christian & Monfort, Alain & Zakoian, Jean-Michel, 2018. "Consistent Pseudo-Maximum Likelihood Estimators and Groups of Transformations," MPRA Paper 87834, University Library of Munich, Germany.
    5. Gabriele Fiorentini & Enrique Sentana, 2018. "Specification tests for non-Gaussian maximum likelihood estimators," Working Paper series 18-22, Rimini Centre for Economic Analysis.
    6. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    7. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper series 38_07, Rimini Centre for Economic Analysis.
    8. Jeroen Rombouts & Marno Verbeek, 2009. "Evaluating portfolio Value-at-Risk using semi-parametric GARCH models," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 737-745.
    9. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    10. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    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. repec:rim:rimwps:38-07 is not listed on IDEAS
    13. Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, vol. 25(02), pages 336-363, April.
    14. Manner, Hans & Türk, Dennis & Eichler, Michael, 2016. "Modeling and forecasting multivariate electricity price spikes," Energy Economics, Elsevier, vol. 60(C), pages 255-265.
    15. 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.
    16. Gabriele Fiorentini & Enrique Sentana, 2012. "Tests for Serial Dependence in Static, Non-Gaussian Factor Models," Working Papers wp2012_1211, CEMFI.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:23:y:2007:i:02:p:251-280_07. 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.

    If CitEc recognized a 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.

    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.