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

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  • Sbrana, Giacomo
  • Poloni, Federico

Abstract

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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Bibliographic Info

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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Related research

Keywords: Multivariate GARCH(1; 1); VARMA; Temporal aggregation; Estimation;

References

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  1. 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).
  2. 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," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153485, Tilburg University.
  3. 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.
  4. Christian M. Hafner, 2004. "Temporal aggregation of multivariate GARCH processes," Econometric Society 2004 North American Winter Meetings 538, Econometric Society.
  5. 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.
  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, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
  8. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  9. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
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