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

Olivier Wintenberger

MPRA Paper from University Library of Munich, Germany

Abstract: 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 (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.

Keywords: Invertible models; volatility models; quasi maximum likelihood; strong consistency; asymptotic normality; exponential GARCH; stochastic recurrence equation. (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2013-01-07
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (71)

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Journal Article: Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model (2013)
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