Estimation and asymptotic properties of a stationary univariate GARCH(p, q) process

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.

Dans ce papier, nous determinons l’Estimateur du Minimum de Distance ´ de Hellinger d’un processus GARCH univarie stationnaire. Nous construisons un ´ estimateur base sur la m ´ ethode du Minimum de Distance de Hellinger. Sous les ´ conditions de φ-melange du processus GARCH, nous ´ etablissons les propri ´ et´ es´ asymptotiques de cet estimateur.

Key words: Hellinger distance estimation; GARCH process; phi-mixing process; consistence; asymptotic normality