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A One Line Derivation of EGARCH


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McAleer, Michael and Hafner, Christian M. (2014) A One Line Derivation of EGARCH. [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 15, 2014, ISSN: 2341-2356 ] (Unpublished)

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Official URL: http://eprints.ucm.es/26051/

Resumen (otros idiomas)

One of the most popular univariate asymmetric conditional volatility models is the exponential GARCH (or EGARCH) specification. In addition to asymmetry, which captures the different effects on conditional volatility of positive and negative effects of equal magnitude, EGARCH can also accommodate leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. However, there are as yet no statistical properties available for the (quasi-) maximum likelihood estimator of the EGARCH parameters. It is often argued heuristically that the reason for the lack of statistical properties arises from the presence in the model of an absolute value of a function of the parameters, which does not permit analytical derivatives or the derivation of statistical properties.It is shown in this paper that: (i)the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process;and (ii) the reason for the lack of statistical properties of the estimators of EGARCH is that the stationarity and invertibility conditions for the RCCNMA process are not known.

Item Type:Working Paper or Technical Report
Additional Information:

For financial support, the first author wishes to acknowledge the Australian Research Council and the National Science Council, Taiwan.

Palabras clave (otros idiomas):Leverage, Asymmetry, Existence, Random coefficient models, Complex nonlinearmoving average process.
Subjects:Social sciences > Economics > Econometrics
JEL:C22, C52, C58, G32
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
ID Code:26051
Deposited On:30 Jun 2014 07:49
Last Modified:30 Jun 2014 07:49

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