GARCH models without positivity constraints: Exponential or log GARCH?

Christian Francq, Olivier Wintenberger and Jean-Michel Zakoian

Journal of Econometrics, 2013, vol. 177, issue 1, 34-46

Abstract: This paper provides a probabilistic and statistical comparison of the log-GARCH and EGARCH models, which both rely on multiplicative volatility dynamics without positivity constraints. We compare the main probabilistic properties (strict stationarity, existence of moments, tails) of the EGARCH model, which are already known, with those of an asymmetric version of the log-GARCH. The quasi-maximum likelihood estimation of the log-GARCH parameters is shown to be strongly consistent and asymptotically normal. Similar estimation results are only available for the EGARCH (1,1) model, and under much stronger assumptions. The comparison is pursued via simulation experiments and estimation on real data.

Keywords: EGARCH; Log-GARCH; Quasi-maximum likelihood; Strict stationarity; Tail index (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (37)

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Related works:
Working Paper: Garch models without positivity constraints: exponential or log garch? (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:177:y:2013:i:1:p:34-46

DOI: 10.1016/j.jeconom.2013.05.004

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