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Estimating multivariate GARCH and stochastic correlation models equation by equation

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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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    References listed on IDEAS

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    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.
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    10. Weide, R. van der, 2002. "Generalized Orthogonal GARCH. A Multivariate GARCH model," CeNDEF Working Papers 02-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    11. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    12. Francq, Christian & Zakoïan, Jean-Michel, 2012. "Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models," Econometric Theory, Cambridge University Press, vol. 28(1), pages 179-206, February.
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    Cited by:

    1. Linton, O. & Wu, J., 2016. "A coupled component GARCH model for intraday and overnight volatility," Cambridge Working Papers in Economics 1671, Faculty of Economics, University of Cambridge.
    2. 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.

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    More about this item

    Keywords

    Constant conditional correlation; Dynamic conditional correlation; Markov switching models; Multivariate GARCH; Quasi maximum likelihood estimation;
    All these keywords.

    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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