Estimating 2-D GARCH models by quasi-maximum of likelihood

Soumia Kharfouchi and Wafa Mili

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 17, 6275-6286

Abstract: In this article, a quasi-maximum of likelihood approach, with minimal assumptions and computational performances, is proposed to estimate the coefficients of the two dimensionally indexed Generalized Autoregressive model. First, sufficient conditions of the existence of a strict stationary solution are given. In a second step, we propose consistent estimators of the parameter vector of interest, even if we are in doubt about the distribution, by minimizing the Kullback–Leiber divergence between the true distribution and a misspecified parametric family of hypothesized distribution. Results of numerical simulations are presented at the end.

Date: 2023
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DOI: 10.1080/03610926.2022.2027452

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