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GARCH models without positivity constraints: Exponential or Log GARCH?

Zakoïan, Jean-Michel; Wintenberger, Olivier; Francq, Christian (2013), GARCH models without positivity constraints: Exponential or Log GARCH?, Journal of Econometrics, 177, 1, p. 34-46. http://dx.doi.org/10.1016/j.jeconom.2013.05.004

Type
Article accepté pour publication ou publié
Date
2013
Journal name
Journal of Econometrics
Volume
177
Number
1
Publisher
Elsevier
Pages
34-46
Publication identifier
http://dx.doi.org/10.1016/j.jeconom.2013.05.004
Metadata
Show full item record
Author(s)
Zakoïan, Jean-Michel
Wintenberger, Olivier
Francq, Christian
Abstract (EN)
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 particular EGARCH models, and under much stronger assumptions. The comparison is pursued via simulation experiments and estimation on real data.
Subjects / Keywords
Tail index; Strict stationarity; Quasi-Maximum Likelihood; log-GARCH; EGARCH
JEL
C13 - Estimation: General
C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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