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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.

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Bibliographic Info

Paper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 2003-21.

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Date of creation: 06 Aug 2003
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Handle: RePEc:ems:eureir:1721

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Keywords: multivariate GARCH models; quasi maximum likelihood;

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References

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  1. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 84(1), pages 61-84, January.
  2. Lucchetti, Riccardo, 2002. "Analytical Score for Multivariate GARCH Models," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 19(2), pages 133-43, April.
  3. Robert F. Engle & Victor Ng & Michael Rothschild, 1988. "Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0065, National Bureau of Economic Research, Inc.
  4. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(1), pages 116-31, February.
  5. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
  7. Herwartz, Helmut & Neumann, Michael H., 2005. "Bootstrap inference in systems of single equation error correction models," Journal of Econometrics, Elsevier, Elsevier, vol. 128(1), pages 165-193, September.
  8. Christian M. Hafner & Helmut Herwartz, 2000. "Testing for linear autoregressive dynamics under heteroskedasticity," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 3(2), pages 177-197.
  9. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 21(4), pages 532-46, October.
  10. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
  11. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 0549, Institute of Social and Economic Research, Osaka University.
  12. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 14(01), pages 70-86, February.
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Cited by:
  1. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 25, pages 61-75, January.
  2. Michael McAleer & Massimiliano Caporin, 2011. "Ranking Multivariate GARCH Models by Problem Dimension:An Empirical Evaluation," KIER Working Papers, Kyoto University, Institute of Economic Research 778, Kyoto University, Institute of Economic Research.
  3. Martin Burda & John Maheu, 2011. "Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models," Working Papers, University of Toronto, Department of Economics tecipa-438, University of Toronto, Department of Economics.
  4. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," "Marco Fanno" Working Papers, Dipartimento di Scienze Economiche "Marco Fanno" 0124, Dipartimento di Scienze Economiche "Marco Fanno".
  5. Hafner, Christian M. & Herwartz, Helmut, 2004. "Testing for Causality in Variance using Multivariate GARCH Models," Economics Working Papers 2004,03, Christian-Albrechts-University of Kiel, Department of Economics.
  6. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3153-3181.
  7. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  8. 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, Econometric Research Association, vol. 1(1), pages 50-62, April.
  9. Tomasz Wozniak, 2012. "Testing Causality Between Two Vectors in Multivariate GARCH Models," Department of Economics - Working Papers Series, The University of Melbourne 1139, The University of Melbourne.
  10. K. Diamantopoulos & I. Vrontos, 2010. "A Student-t Full Factor Multivariate GARCH Model," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 35(1), pages 63-83, January.
  11. Chrétien, Stéphane & Ortega, Juan-Pablo, 2014. "Multivariate GARCH estimation via a Bregman-proximal trust-region method," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 210-236.

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