Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model


  • Olivier Wintenberger

    Corresponding author
    1. CEREMADE, Université de Paris-Dauphine & LFA, CREST
    • Olivier Wintenberger, Centre De Recherche en Mathématiques de la Décision, Université de Paris-Dauphine, UMR CNRS 7534, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France.


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I introduce the notion of continuous invertibility on a compact set for volatility models driven by a stochastic recurrence equation. I prove strong consistency of the quasi-maximum likelihood estimator (QMLE) when the quasi-likelihood criterion is maximized on a continuously invertible domain. This approach yields, for the first time, the asymptotic normality of the QMLE for the exponential general autoregressive conditional heteroskedastic (EGARCH(1,1)) model under explicit but non-verifiable conditions. In practice, I propose to stabilize the QMLE by constraining the optimization procedure to an empirical continuously invertible domain. The new method, called stable QMLE, is asymptotically normal when the observations follow an invertible EGARCH(1,1) model.