Template-type: ReDIF-Paper 1.0
Author-Name: Michael McAleer
Author-Person: pmc90 
Author-Workplace-Name: Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute,
	The Netherlands, Department of Quantitative Economics, Complutense University of Madrid, and Institute of
	Economic Research, Kyoto University. 
Author-Name: Christian M. Hafner 

Author-Email: christian.hafner@uclouvain.be
Author-Person: pha77
Author-Workplace-Name: Institut de statistique, biostatistique et sciences actuarielles Université catholique de Louvain 

Title: A One Line Derivation of EGARCH
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.
Note: For financial support, the first author wishes to acknowledge the Australian Research Council and the National Science Council, 
	Taiwan.
Classification-JEL: C22, C52, C58, G32. 

Length: 8 pages
Creation-Date: 2014-06 
Number: 2014-15 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1415.txt
File-URL: https://eprints.ucm.es/id/eprint/26051/1/1415.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1415