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GARCH models without positivity constraints: Exponential or log GARCH?

  • Francq, Christian
  • Wintenberger, Olivier
  • Zakoïan, Jean-Michel

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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304407613001267
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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 177 (2013)
Issue (Month): 1 ()
Pages: 34-46

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Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:34-46
DOI: 10.1016/j.jeconom.2013.05.004
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  16. Changli He & Timo Terasvirta & Hans Malmsten, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," Research Paper Series 29, Quantitative Finance Research Centre, University of Technology, Sydney.
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