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On the Invertibility of EGARCH(p,q)

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Martinet, Guillaume Gaetan and McAleer, Michael (2015) On the Invertibility of EGARCH(p,q). [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 03, 2015, ISSN: 2341-2356 ] (Unpublished)

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Official URL: http://eprints.ucm.es/28344/




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 estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH(p,q) 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(p,q) parameters.


Item Type:Working Paper or Technical Report
Additional Information:

The authors are grateful to the Editor-in-Chief, Rob Taylor, an Associate Editor and two referees for very helpful comments and suggestions, and to Christian Hafner for insightful 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:2015
Number:03
ID Code:28344
Deposited On:12 Feb 2015 16:32
Last Modified:21 Jan 2016 09:36

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