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Semiparametric multivariate volatility models

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

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.

Suggested Citation

  • Rombouts, Jeroen V. K. & Hafner, Christian M., 2004. "Semiparametric multivariate volatility models," Papers 2004,14, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
  • Handle: RePEc:zbw:caseps:200414
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    Citations

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    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    9. Gabriele Fiorentini & Enrique Sentana, 2018. "Consistent non-Gaussian pseudo maximum likelihood estimators," Econometrics Working Papers Archive 2018_01, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    10. 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.
    11. repec:rim:rimwps:38-07 is not listed on IDEAS
    12. 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.
    13. Manner, Hans & Türk, Dennis & Eichler, Michael, 2016. "Modeling and forecasting multivariate electricity price spikes," Energy Economics, Elsevier, vol. 60(C), pages 255-265.
    14. 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.
    15. Gabriele Fiorentini & Enrique Sentana, 2012. "Tests for Serial Dependence in Static, Non-Gaussian Factor Models," Working Papers wp2012_1211, CEMFI.

    More about this item

    Keywords

    Multivariate volatility; GARCH; semiparametric efficiency; adaptivity;

    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

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