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Asymptotic Theory For A Factor Garch Model

  • Hafner, Christian M.
  • Preminger, Arie

This paper investigates the asymptotic theory for a factor GARCH (generalized autoregressive conditional heteroskedasticity) model. Sufficient conditions for asymptotic stability and existence of moments are established. These conditions allow for volatility spillover 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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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 25 (2009)
Issue (Month): 02 (April)
Pages: 336-363

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Handle: RePEc:cup:etheor:v:25:y:2009:i:02:p:336-363_09
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  1. Lanne, Markku & Saikkonen, Pentti, 2005. "A Multivariate Generalized Orthogonal Factor GARCH Model," MPRA Paper 23714, University Library of Munich, Germany.
  2. Arie Preminger & Giuseppe Storti, 2006. "A Garch (1,1) Estimator With (Almost) No Moment Conditions On The Error Term," Working Papers 0607, Ben-Gurion University of the Negev, Department of Economics.
  3. Rombouts, Jeroen V. K. & Hafner, Christian M., 2004. "Semiparametric multivariate volatility models," Papers 2004,14, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  4. 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.
  5. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Other publications TiSEM aa253902-af93-4e1e-b974-2, Tilburg University, School of Economics and Management.
  6. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  7. 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.
  8. Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," SSE/EFI Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007.
  9. Storti, G., 2006. "Minimum distance estimation of GARCH(1,1) models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1803-1821, December.
  10. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP 1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  12. 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.
  13. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  14. 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.
  15. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  16. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  17. 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.
  18. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
  19. 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.
  20. 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.
  21. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  22. I. D. Vrontos & P. Dellaportas & D. N. Politis, 2003. "A full-factor multivariate GARCH model," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 312-334, December.
  23. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  24. 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.
  25. 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.
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