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A One Line Derivation of EGARCH

Michael McAleer and Christian Hafner ()

Working Papers in Economics from University of Canterbury, Department of Economics and Finance

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 nonlinear moving average process (search for similar items in EconPapers)
JEL-codes: C22 C52 C58 G32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Date: 2014-06-16
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http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/1416.pdf (application/pdf)

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Journal Article: A One Line Derivation of EGARCH (2014) Downloads
Working Paper: A One Line Derivation of EGARCH (2014) Downloads
Working Paper: A One Line Derivation of EGARCH (2014) Downloads
Working Paper: A One Line Derivation of EGARCH (2014) Downloads
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