Econometrics 2014, 2(2), 92-97; doi:10.3390/econometrics2020092
Article

A One Line Derivation of EGARCH

1,2,3,4,* email and 5email
Received: 16 June 2014; in revised form: 19 June 2014 / Accepted: 20 June 2014 / Published: 23 June 2014
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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, the statistical properties of the (quasi-) maximum likelihood estimator of the EGARCH parameters are not available under general conditions, but rather only for special cases under highly restrictive and unverifiable conditions. It is often argued heuristically that the reason for the lack of general 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, and hence does not permit (quasi-) maximum likelihood estimation. It is shown in this paper for the non-leverage case that: (1) the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process; and (2) the reason for the lack of statistical properties of the estimators of EGARCH under general conditions is that the stationarity and invertibility conditions for the RCCNMA process are not known.
Keywords: leverage; asymmetry; existence; random coefficient models; complex non-linear moving average process
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MDPI and ACS Style

McAleer, M.; Hafner, C.M. A One Line Derivation of EGARCH. Econometrics 2014, 2, 92-97.

AMA Style

McAleer M, Hafner CM. A One Line Derivation of EGARCH. Econometrics. 2014; 2(2):92-97.

Chicago/Turabian Style

McAleer, Michael; Hafner, Christian M. 2014. "A One Line Derivation of EGARCH." Econometrics 2, no. 2: 92-97.

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