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Analytical quasi maximum likelihood inference in multivariate volatility models

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  • Hafner, C.M.
  • Herwartz, H.

Abstract

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian and show in a simulation study that they clearly outperform numerical methods. As an example, we use the popular BEKK-GARCH model, for which we derive first and second order derivatives.

Suggested Citation

  • Hafner, C.M. & Herwartz, H., 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Research Papers EI 2003-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:1721
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    Cited by:

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    3. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    4. Fengler, Matthias R. & Herwartz, Helmut, 2015. "Measuring spot variance spillovers when (co)variances are time-varying – the case of multivariate GARCH models," Economics Working Paper Series 1517, University of St. Gallen, School of Economics and Political Science.
    5. Christian M. Hafner & Helmut Herwartz, 2009. "Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 294-323, August.
    6. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CARF F-Series CARF-F-219, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Christian M. Hafner & Helmut Herwartz, 2008. "Testing for Causality in Variance Usinf Multivariate GARCH Models," Annals of Economics and Statistics, GENES, issue 89, pages 215-241.
    8. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
    9. 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.
    10. Burda Martin, 2015. "Constrained Hamiltonian Monte Carlo in BEKK GARCH with Targeting," Journal of Time Series Econometrics, De Gruyter, vol. 7(1), pages 1-19, January.
    11. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    12. Monica Billio & Massimiliano Caporin & Lorenzo Frattarolo & Loriana Pelizzon, 2016. "Networks in risk spillovers: a multivariate GARCH perspective," Working Papers 2016:03, Department of Economics, University of Venice "Ca' Foscari".
    13. Chrétien, Stéphane & Ortega, Juan-Pablo, 2014. "Multivariate GARCH estimation via a Bregman-proximal trust-region method," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 210-236.
    14. Wasel Shadat & Chris Orme, 2011. "An investigation of parametric tests of CCC assumption," Economics Discussion Paper Series 1109, Economics, The University of Manchester.
    15. Walid Ben Omrane & Christian M. Hafner, 2009. "Information Spillover, Volatility and the Currency Markets for the Binary Choice Model," International Econometric Review (IER), Econometric Research Association, vol. 1(1), pages 50-62, April.
    16. Xiaochun Liu, 2018. "Structural Volatility Impulse Response Function and Asymptotic Inference," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(2), pages 316-339.
    17. Martin Burda & John Maheu, 2011. "Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models," Working Papers tecipa-438, University of Toronto, Department of Economics.
    18. Fengler, Matthias & Polivka, Jeannine, 2021. "Identifying structural shocks to volatility through a proxy-MGARCH model," Economics Working Paper Series 2103, University of St. Gallen, School of Economics and Political Science, revised May 2021.
    19. K. Diamantopoulos & I. Vrontos, 2010. "A Student-t Full Factor Multivariate GARCH Model," Computational Economics, Springer;Society for Computational Economics, vol. 35(1), pages 63-83, January.
    20. Poloni, Federico & Sbrana, Giacomo, 2014. "Feasible generalized least squares estimation of multivariate GARCH(1, 1) models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 151-159.
    21. Jonathan Dark & Xibin Zhang & Nan Qu, 2010. "Influence diagnostics for multivariate GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 278-291, July.
    22. Gatfaoui, Hayette, 2013. "Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets," Economic Modelling, Elsevier, vol. 30(C), pages 776-791.

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    More about this item

    Keywords

    multivariate GARCH models; quasi maximum likelihood;

    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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