Template-type: ReDIF-Paper 1.0
Author-Name: Chia-Lin Chang
Author-Workplace-Name: Department of Applied Economics Department of Finance National Chung Hsing University Taichung, Taiwan.
Author-Name:
 Michael McAleer
Author-Workplace-Name:
 Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute Erasmus School of 
	Economics Erasmus University Rotterdam, The Netherlands and Department of Quantitative Economics Complutense University of 
	Madrid, Spain And Institute of Advanced Sciences Yokohama National University, Japan.
Title: The Correct Regularity Condition and Interpretation of Asymmetry in EGARCH
Abstract: In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional 
	heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and 
	Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularity 
	properties, including invertibility, to determine the likelihood function for estimation, and the statistical conditions to establish 
	asymptotic properties, it is convenient to understand the stochastic properties underlying the three univariate models. The random 
	coefficient autoregressive process was used to obtain GARCH by Tsay (1987), an extension of which was used by McAleer (2004) to obtain 
	GJR. A random coefficient complex nonlinear moving average process was used by McAleer and Hafner (2014) to obtain EGARCH. These models 
	can be used to capture asymmetry, which denotes the different effects on conditional volatility of positive and negative effects of 
	equal magnitude, and possibly also leverage, which is the negative correlation between returns shocks and subsequent shocks to 
	volatility (see Black 1979). McAleer (2014) showed that asymmetry was possible for GJR, but not leverage. McAleer and Hafner showed 
	that leverage was not possible for EGARCH. Surprisingly, the conditions for asymmetry in EGARCH seem to have been ignored in the 
	literature, or have concentrated on the incorrect conditions, with no clear explanation, and hence with associated misleading 
	interpretations. The purpose of the paper is to derive the regularity condition for asymmetry in EGARCH to provide the correct 
	interpretation. It is shown that, in practice, EGARCH always displays asymmetry, though not leverage.
Classification-JEL: C22, C52, C58, G32.
Keywords: Conditional volatility models, Random coefficient complex nonlinear moving average process, EGARCH, Asymmetry, Leverage, Regularity 
	condition.
Length: 10 pages 
Creation-Date: 2017-06
Number: 2017-17
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1717.txt
File-URL: https://eprints.ucm.es/id/eprint/43463/1/1717.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1717