Revisiting Several Popular GARCH Models with Leverage Effect: Differences and Similarities

In this paper, we analyze five of the most popular models proposed to represent conditional heteroscedasticity with leverage effect, namely, GQARCH, TGARCH, GJR, EGARCH, and APARCH. We show that when the parameters satisfy the positivity, stationarity, and finite kurtosis conditions, the dynamics that the GJR and GQARCH models can represent are heavily limited while those of the TGARCH and EGARCH models are less restricted. Alternatively, when the parameters of the GQARCH and GJR models are estimated without restrictions, one can often conclude that the unconditional variance or kurtosis of returns do not exist even when they truly do. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.