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

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

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 20, 10253-10271

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.

Date: 2017
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DOI: 10.1080/03610926.2016.1231824

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