A One Line Derivation of EGARCH

Michael McAleer and Christian Hafner

No 2014-15, Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

Abstract: 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.

Keywords: Leverage; Asymmetry; Existence; Random coefficient models; Complex nonlinearmoving average process. (search for similar items in EconPapers)
JEL-codes: C22 C52 C58 G32 (search for similar items in EconPapers)
Pages: 8 pages
Date: 2014-06
New Economics Papers: this item is included in nep-ore
Note: For financial support, the first author wishes to acknowledge the Australian Research Council and the National Science Council, Taiwan.
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Related works:
Journal Article: A One Line Derivation of EGARCH (2014)
Working Paper: A One Line Derivation of EGARCH (2014)
Working Paper: A One Line Derivation of EGARCH (2014)
Working Paper: A One Line Derivation of EGARCH (2014)
Working Paper: A One Line Derivation of EGARCH (2014)
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