Template-type: ReDIF-Paper 1.0
Author-Name: Guillaume Gaetan Martinet
Author-Workplace-Name: ENSAE Paris Tech, France, and Columbia University, United States.
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. 
Title: On the Invertibility of EGARCH
Abstract: Of the two most widely estimated univariate asymmetric conditional volatility models, the 
	exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the 
	different effects on conditional volatility of positive and negative effects of equal magnitude, and 
	leverage, which refers to the negative correlation between the returns shocks and subsequent 
	shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood 
	estimator (QMLE) of the EGARCH parameters are not available under general conditions, but 
	only for special cases under highly restrictive and unverifiable conditions. A limitation in the 
	development of asymptotic properties of the QMLE for EGARCH is the lack of an invertibility 
	condition for the returns shocks underlying the model. It is shown in this paper that the 
	EGARCH model can be derived from a stochastic process, for which the invertibility conditions 
	can be stated simply and explicitly. This will be useful in re-interpreting the existing properties 
	of the QMLE of the EGARCH parameters. 
Classification-JEL: C22, C52, C58, G32.
Keywords:  Leverage, Asymmetry, Existence, Stochastic process, Asymptotic properties, Invertibility.
Note: The authors are grateful to Christian Hafner for very helpful discussions. For financial support, 
	the first author wishes to thank the National Science Council, Taiwan, and the second author is 
	most grateful to the Australian Research Council and the National Science Council, Taiwan.
Length: 14 pages
Creation-Date: 2014
Number: 2014-28 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1428.txt
File-URL: https://eprints.ucm.es/id/eprint/27158/1/1428.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1428