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Continuous invertibility and stable QML estimation of the EGARCH(1,1) model

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Date
2013
Link to item file
http://hal.archives-ouvertes.fr/hal-00751706
Dewey
Probabilités et mathématiques appliquées
Sujet
stochastic recurrence equation; exponential GARCH; asymptotic normality; strong consistency; quasi maximum likelihood; volatility models; Invertible models
Journal issue
Scandinavian Journal of Statistics
Volume
40
Number
4
Publication date
2013
Article pages
846-867
Publisher
Wiley
DOI
http://dx.doi.org/10.1111/sjos.12038
URI
https://basepub.dauphine.fr/handle/123456789/10825
Collections
  • CEREMADE : Publications
Metadata
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Author
Wintenberger, Olivier
Type
Article accepté pour publication ou publié
Abstract (EN)
We introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE). We prove the strong consistency of the Quasi Maximum Likelihood Estimator (QMLE) when the optimization procedure is done on a continuously invertible domain. 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 under explicit but non observable conditions. In practice, we propose to stabilize the QMLE by constraining the optimization procedure to an empirical continuously invertible domain. The new method, called Stable QMLE (SQMLE), is strongly consistent when the observations follow an invertible EGARCH(1,1) model. We also give the asymptotic normality of the SQMLE under additional minimal assumptions.

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