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Estimating multivariate GARCH and stochastic correlation models equation by equation

Author

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  • Francq, Christian
  • Zakoian, Jean-Michel

Abstract

A new approach is proposed to estimate a large class of multivariate volatility models. The method is based on estimating equation-by-equation the volatility parameters of the individual returns by quasi-maximum likelihood in a first step, and estimating the correlations based on volatility-standardized returns in a second step. Instead of estimating a $d$-multivariate volatility model we thus estimate $d$ univariate GARCH-type equations plus a correlation matrix, which is generally much simpler and numerically efficient. The strong consistency and asymptotic normality of the first-step estimator is established in a very general framework. For generalized constant conditional correlation models, and also for some time-varying conditional correlation models, we obtain the asymptotic properties of the two-step estimator. Our estimator can also be used to test the restrictions imposed by a particular MGARCH specification. An application to financial series illustrates the interest of the approach.

Suggested Citation

  • Francq, Christian & Zakoian, Jean-Michel, 2014. "Estimating multivariate GARCH and stochastic correlation models equation by equation," MPRA Paper 54250, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:54250
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    File URL: https://mpra.ub.uni-muenchen.de/54250/1/MPRA_paper_54250.pdf
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    References listed on IDEAS

    as
    1. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    2. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    6. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    7. Robert Engle & Neil Shephard & Kevin Shepphard, 2008. "Fitting vast dimensional time-varying covariance models," OFRC Working Papers Series 2008fe30, Oxford Financial Research Centre.
    8. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    11. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
    12. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Ahmed El Ghini & Youssef Saidi, 2017. "Return and volatility spillovers in the Moroccan stock market during the financial crisis," Empirical Economics, Springer, vol. 52(4), pages 1481-1504, June.

    More about this item

    Keywords

    Constant conditional correlation; Dynamic conditional correlation; Markov switching models; Multivariate GARCH; Quasi maximum likelihood estimation;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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