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

Wintenberger, Olivier (2013), Continuous invertibility and stable QML estimation of the EGARCH(1,1) model, Scandinavian Journal of Statistics, 40, 4, p. 846-867. http://dx.doi.org/10.1111/sjos.12038

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00751706
Date
2013
Journal name
Scandinavian Journal of Statistics
Volume
40
Number
4
Publisher
Wiley
Pages
846-867
Publication identifier
http://dx.doi.org/10.1111/sjos.12038
Metadata
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Author(s)
Wintenberger, Olivier
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.
Subjects / Keywords
stochastic recurrence equation; exponential GARCH; asymptotic normality; strong consistency; quasi maximum likelihood; volatility models; Invertible models

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