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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, vol. 84(1), pages 61-84, January.
  2. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  3. Riccardo LUCCHETTI, 1999. "Analytic Score for Multivariate GARCH Models," Working Papers 119, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
  4. 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.
  5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  6. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  7. Christian M. Hafner & Helmut Herwartz, 2000. "Testing for linear autoregressive dynamics under heteroskedasticity," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 177-197.
  8. Herwartz, Helmut & Neumann, Michael H., 2005. "Bootstrap inference in systems of single equation error correction models," Journal of Econometrics, Elsevier, vol. 128(1), pages 165-193, September.
  9. 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, vol. 96(1), pages 116-31, February.
  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. 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, vol. 21(4), pages 532-46, October.
  12. 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 0065, National Bureau of Economic Research, Inc.
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Cited by:
  1. K. Diamantopoulos & I. Vrontos, 2010. "A Student-t Full Factor Multivariate GARCH Model," Computational Economics, Society for Computational Economics, vol. 35(1), pages 63-83, January.
  2. Christian M. HAFNER & Helmut HERWARTZ, 2008. "Testing for Causality in Variance Usinf Multivariate GARCH Models," Annales d'Economie et de Statistique, ENSAE, issue 89, pages 215-241.
  3. Michael McAleer & Massimiliano Caporin, 2011. "Ranking Multivariate GARCH Models by Problem Dimension:An Empirical Evaluation," KIER Working Papers 778, Kyoto University, Institute of Economic Research.
  4. 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.
  5. 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.
  6. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
  7. Lanne, Markku & Saikkonen, Pentti, 2005. "A Multivariate Generalized Orthogonal Factor GARCH Model," MPRA Paper 23714, University Library of Munich, Germany.
  8. Tomasz Wozniak, 2012. "Testing Causality Between Two Vectors in Multivariate GARCH Models," Department of Economics - Working Papers Series 1139, The University of Melbourne.
  9. 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.
  10. 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.
  11. 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.

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