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Asymptotic theory for a factor GARCH model

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  • HAFNER, Christian M.
  • PREMINGER, Arie

Abstract

This paper investigates the asymptotic theory for a factor GARCH model. Sufficient conditions for strict stationarity, existence of certain moments, geometric ergodicity and - mixing with exponential decay rates are established. These conditions allow for volatility spill-over and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the model parameters. The results are obtained under the finiteness of the fourth order moment of the innovations.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006071.

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Date of creation: 00 Sep 2006
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Handle: RePEc:cor:louvco:2006071

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Keywords: multivariate GARCH; factor model; geometric ergodicity; maximum likelihood; consistency; asymptotic normality;

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References

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  1. Christian Francq & Jean-Michel Zakoïan, 2006. "Inference in GARCH when some coefficients are equal to zero," Computing in Economics and Finance 2006 64, Society for Computational Economics.
  2. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  3. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74145, Tilburg University.
  4. Storti, G., 2006. "Minimum distance estimation of GARCH(1,1) models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1803-1821, December.
  5. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  6. PREMINGER, Arie & STORTI, Giuseppe, 2006. "A GARCH (1,1) estimator with (almost) no moment conditions on the error term," CORE Discussion Papers 2006068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  8. Hafner, C.M. & Rombouts, J.V.K., 2004. "Semiparametric multivariate volatility models," Econometric Institute Research Papers EI 2004-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  9. 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.
  10. Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007.
  11. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  12. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  13. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
  14. Lanne, Markku & Saikkonen, Pentti, 2005. "A Multivariate Generalized Orthogonal Factor GARCH Model," MPRA Paper 23714, University Library of Munich, Germany.
  15. 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.
  16. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  17. Kristensen, Dennis & Linton, Oliver, 2006. "A Closed-Form Estimator For The Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 22(02), pages 323-337, April.
  18. Francq, Christian & Zako an, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, vol. 22(05), pages 815-834, October.
  19. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
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Citations

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Cited by:
  1. Hecq Alain & Laurent Sébastien & Palm Franz C., 2012. "On the Univariate Representation of BEKK Models with Common Factors," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Marco Avarucci & Eric Beutner & Paolo Zaffaroni, 2012. "On moment conditions for quasi-maximum likelihood estimation of multivariate ARCH models," DSS Empirical Economics and Econometrics Working Papers Series 2012/1, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
  3. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2013. "Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown," MPRA Paper 49344, University Library of Munich, Germany.
  4. Palandri, Alessandro, 2009. "Sequential conditional correlations: Inference and evaluation," Journal of Econometrics, Elsevier, vol. 153(2), pages 122-132, December.
  5. Yip, Iris W.H. & So, Mike K.P., 2009. "Simplified specifications of a multivariate generalized autoregressive conditional heteroscedasticity model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 327-340.
  6. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
  7. Francq, Christian & Zakoian, Jean-Michel, 2010. "QML estimation of a class of multivariate GARCH models without moment conditions on the observed process," MPRA Paper 20779, University Library of Munich, Germany.

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