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On the Invertibility of EGARCH

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Martinet, Guillaume Gaetan and McAleer, Michael (2014) On the Invertibility of EGARCH. [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 28, 2014, ISSN: 2341-2356 ] (Unpublished)

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Abstract

Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimators (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions. A limitation in the development of asymptotic properties of the QMLE for EGARCH is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH parameters.


Item Type:Working Paper or Technical Report
Additional Information:

The authors are grateful to Christian Hafner for very helpful discussions. For financial support, the first author wishes to thank the National Science Council, Taiwan, and the second author is most grateful to the Australian Research Council and the National Science Council, Taiwan.

Uncontrolled Keywords:Leverage, asymmetry, Existence, Stochastic process, asymptotic properties, Invertibility.
Subjects:Social sciences > Economics > Econometrics
JEL:C22, C52, C58, G32
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
Volume:2014
Number:28
ID Code:27158
Deposited On:04 Nov 2014 09:37
Last Modified:21 Jan 2016 12:44

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