Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/98887
Authors: 
McAleer, Michael
Hafner, Christian M.
Year of Publication: 
2014
Series/Report no.: 
Tinbergen Institute Discussion Paper 14-069/III
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.
Subjects: 
Leverage
asymmetry
existence
random coefficient models
complex nonlinear moving average process
JEL: 
C22
C52
C58
G32
Document Type: 
Working Paper

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