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Pseudo maximum-likelihood estimation of the univariate GARCH (1,1) and asymptotic properties

Author

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  • Eugene Kouassi
  • Patrice Takam Soh
  • Jean Marcelin Bosson Brou
  • Emile Herve Ndoumbe

Abstract

One provides in this paper the pseudo-likelihood estimator (PMLE) and asymptotic theory for the GARCH (1,1) process. Strong consistency of the pseudo-maximum-likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau (1998) concerning the existence of a stationary and ergodic solution to the multivariate GARCH (p, q) process. One proves the asymptotic normality of the PMLE by appealing to martingales' techniques.

Suggested Citation

  • Eugene Kouassi & Patrice Takam Soh & Jean Marcelin Bosson Brou & Emile Herve Ndoumbe, 2017. "Pseudo maximum-likelihood estimation of the univariate GARCH (1,1) and asymptotic properties," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10253-10271, October.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:20:p:10253-10271
    DOI: 10.1080/03610926.2016.1231824
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    Cited by:

    1. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.

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