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A closed-form estimator for the multivariate GARCH(1,1) model

  • Sbrana, Giacomo
  • Poloni, Federico

We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1) model. We show that the GARCH parameters can be derived analytically, using the autocovariances of the observed data, applying simple linear algebra tools. The resulting estimator is consistent and asymptotically normally distributed.

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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 120 (2013)
Issue (Month): C ()
Pages: 152-162

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Handle: RePEc:eee:jmvana:v:120:y:2013:i:c:p:152-162
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  1. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  2. 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.
  3. 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.
  4. 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.
  5. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  6. repec:ner:tilbur:urn:nbn:nl:ui:12-153485 is not listed on IDEAS
  7. Engwerda, J.C. & Ran, A.C.M. & Rijkeboer, A.L., 1993. "Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X + A*X-1A = Q," Other publications TiSEM 70617266-94a2-4f19-9d69-e, Tilburg University, School of Economics and Management.
  8. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  9. Hafner, C.M., 2004. "Temporal aggregation of multivariate GARCH processes," Econometric Institute Research Papers EI 2004-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  10. 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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