Template-type: ReDIF-Paper 1.0
Author-Name: Guillaume Gaetan Martinet 
Author-Workplace-Name: ENSAE Paris Tech, France
Author-Workplace-Name: Department of Industrial Engineering and Operations Research Columbia University, USA
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(p,q)
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, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of 
	asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks 
	underlying the model. It is shown in this paper that the EGARCH(p,q) 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(p,q) parameters.
Classification-JEL: C22, C52, C58, G32.
Keywords:  Leverage, asymmetry, Existence, Stochastic process, Asymptotic properties, Invertibility.
Note: The authors are grateful to the Editor-in-Chief, Rob Taylor, an Associate Editor and two referees for very helpful comments and 
	suggestions, and to Christian Hafner for insightful 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: 47 pages
Creation-Date: 2015-02  
Number: 2015-03 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1503.txt
File-URL: https://eprints.ucm.es/id/eprint/28344/1/1503.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1503