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Estimation and asymptotic properties of a stationary univariate GARCH(\(p,q\)) process. (English. French summary) Zbl 1445.62230

Summary: 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 phi-mixing of the GARCH process, we establish the almost sure convergence and the asymptotic normality of the estimator.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62G35 Nonparametric robustness
60G10 Stationary stochastic processes
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References:

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