Abstract: In this paper, we determine the Minimum Hellinger Distance estimator of a stationary univariate GARCH process. We construct an estimator of the parameters based on the minimum Hellinger distance method. Under conditions which ensure the φ-mixing of the GARCH process, we establish the almost sure convergence and the asymptotic normality of the estimator.

Key words: Hellinger distance estimation; GARCH process; phi-mixing process;
consistence; asymptotic normality.
AMS 2010 Mathematics Subject Classification : 62F12, 62G35, 62H12, 60G10.

Aka Roger Kadjo (1,2,∗), Ouagnina Hili (2) and Aubin N’dri (2,3)
(1) University Felix Houphouët-Boigny, Abidjan-Cocody, Côte d’Ivoire. 
(2) Laboratory of Mathematics and New Technologies of Information, National Polytechnic Institute Felix Houphouet-Boigny, BP 1911, Yamoussoukro, Cote d’Ivoire. 
(3) University Jean Lorougnon Guédé, Cote d’Ivoire. 

Received July 24,2019; Accepted January 28, 2020
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