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Consistent Estimation for Aggregated GARCH

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  • Komunjer, Ivana

Abstract

We study the properties of a quasi-maximum likelihood (QML) for the parameters of a "weak" GARCH process obtained by contemporaneous aggregation of two independent "strong" GARCH processes. The inconsistency of the Gaussian quasi-likelihood estimator (QMLE) has already been reported by Nijman & Sentana (1996) but has not yet been solved. In this paper we identify the causes of inconsistency of QMLE in the "weak" GARCH case and compare the performance of QMLE when the innovations are assumed to have Gaussian, Laplace (double exponential) or alpha-stable distribution.

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Bibliographic Info

Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt1fp2v3q7.

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Date of creation: 01 May 2001
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Handle: RePEc:cdl:ucsdec:qt1fp2v3q7

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Keywords: aggregation; GARCH; estimation; quasi-maximum likelihood; consistency;

References

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  1. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153273, Tilburg University.
  2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  3. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
  4. Nijman, T.E. & Sentana, E., 1993. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Discussion Paper 1993-12, Tilburg University, Center for Economic Research.
  5. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 243-247, December.
  6. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  9. 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.
  10. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
  11. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
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