QML estimation of the continuously invertible EGARCH(1,1) model
Résumé
We introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE) introduced by Straumann in \cite{straumann:2005}. We prove the strong consistency of the Quasi Maximum Likelihood Estimator (QMLE) for such continuously invertible models. This approach gives for the first time the strong consistency of the QMLE used by Nelson in \cite{nelson:1991} for the EGARCH(1,1) model. We also give sufficient conditions for the asymptotic normality of the QMLE for this model. We propose a new estimator IQMLE with the same asymptotic properties than QMLE but for which the volatility forecasting is stable.
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