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Semiparametric multivariate GARCH models

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  • HAFNER, Christian
  • ROMBOUTS, Jeroen

Abstract

Estimation of multivariate GARCH models is usually carried out by quasi maximum likelihood (QMLE), for which recently consistency and asymptotic normality have been proven under quite general conditions. However, there are to date no results on the efficiency loss of QMLE if the true innovation distribution is not multinormal. We investigate this issue by suggesting a nonparametric estimation of the multivariate innovation distribution, based on consistent parameter estimates obtained by QMLE. We give conditions under which the semiparametric efficiency bound can be attained. A simulation experiment demonstrates the efficiency gain of our procedure compared with QMLE, and an application to a bivariate stock index series illustrates the results.

Suggested Citation

  • HAFNER, Christian & ROMBOUTS, Jeroen, 2003. "Semiparametric multivariate GARCH models," LIDAM Discussion Papers CORE 2003003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2003003
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    References listed on IDEAS

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    1. 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.
    2. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    3. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(4), pages 539-569, August.
    4. 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.
    5. 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.
    6. Gloria Gonzalez-Rivera, 1997. "A note on adaptation in garch models," Econometric Reviews, Taylor & Francis Journals, vol. 16(1), pages 55-68.
    7. 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.
    8. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
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    1. HAFNER, Christian & ROMBOUTS, Jeroen, 2003. "Estimation of temporally aggregated multivariate GARCH models," LIDAM Discussion Papers CORE 2003073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    multivariate GARCH models; semiparametric methods; efficient estimation;
    All these keywords.

    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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