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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.

Suggested Citation

  • Komunjer, Ivana, 2001. "Consistent Estimation for Aggregated GARCH," University of California at San Diego, Economics Working Paper Series qt1fp2v3q7, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt1fp2v3q7
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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. 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 137-158, February.
    4. 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.
    5. Nijman, Theo & Sentana, Enrique, 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 71-87.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. 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.
    8. 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.
    9. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
    10. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Jondeau, Eric, 2015. "The dynamics of squared returns under contemporaneous aggregation of GARCH models," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 80-93.
    2. repec:eee:ecolet:v:156:y:2017:i:c:p:110-113 is not listed on IDEAS
    3. Eric Jondeau, 2008. "Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias," Swiss Finance Institute Research Paper Series 08-06, Swiss Finance Institute.

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