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AN ALMOST CLOSED FORM ESTIMATOR FOR THE EGARCH MODEL

Published online by Cambridge University Press:  22 August 2016

Christian M. Hafner*
Affiliation:
Université catholique de Louvain
Oliver Linton
Affiliation:
University of Cambridge
*
*Address correspondence to Christian M. Hafner, CORE and Institut de statistique, biostatistique et sciences actuarielles, Université catholique de Louvain, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium; e-mail: christian.hafner@uclouvain.be.

Abstract

The exponential GARCH (EGARCH) model introduced by Nelson (1991) is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference are usually done via maximum likelihood. Although some progress has been made recently, a complete distribution theory of MLE for EGARCH models is still missing. Furthermore, the estimation procedure itself may be highly sensitive to starting values, the choice of numerical optimization algorithm, etc. We present an alternative estimator that is available in a simple closed form and which could be used, for example, as starting values for MLE. The estimator of the dynamic parameter is independent of the innovation distribution. For the other parameters we assume that the innovation distribution belongs to the class of Generalized Error Distributions (GED), profiling out its parameter in the estimation procedure. We discuss the properties of the proposed estimator and illustrate its performance in a simulation study and an empirical example.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

We thank Eric Renault, Piotr Fryzlewicz, Dimitra Kyriakopoulou, Enno Mammen, Paolo Zaffaroni, Jean-Michel Zakoian, and three referees for helpful comments. Financial support of the Académie universitaire Louvain is gratefully acknowledged. Thanks to the ERC for financial support.

References

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