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GARCH models without positivity constraints: Exponential or Log GARCH?

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

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.

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Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/10571.

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Date of creation: 2013
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Publication status: Published in Journal of Econometrics, 2013, Vol. 177, no. 1. pp. 34-46.Length: 12 pages
Handle: RePEc:dau:papers:123456789/10571
Contact details of provider: Web page: http://www.dauphine.fr/en/welcome.html

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  1. BAUWENS, Luc & GIOT, Pierre, . "Asymmetric ACD models: Introducing price information in ACD models," CORE Discussion Papers RP 1670, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  5. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
  6. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  7. Christian Francq & Jean-Michel Zakoïan, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Post-Print hal-00732536, HAL.
  8. Luc Bauwens & Pierre Giot & Joachim Grammig & David Veredas, 2004. "A comparison of financial duration models via density forecast," ULB Institutional Repository 2013/136218, ULB -- Universite Libre de Bruxelles.
  9. Luc BAUWENS & Pierre GIOT, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annales d'Economie et de Statistique, ENSAE, issue 60, pages 117-149.
  10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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  13. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
  14. Genaro Sucarrat & Alvaro Escribano, 2012. "Automated Model Selection in Finance: General-to-Specific Modelling of the Mean and Volatility Specifications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(5), pages 716-735, October.
  15. 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.
  16. Kristensen Dennis & Rahbek Anders, 2009. "Asymptotics of the QMLE for Non-Linear ARCH Models," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-38, April.
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  18. Wintenberger, Olivier, 2013. "Continuous invertibility and stable QML estimation of the EGARCH(1,1) model," MPRA Paper 46027, University Library of Munich, Germany.
  19. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
  20. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
  21. Wintenberger, Olivier & Cai, Sixiang, 2011. "Parametric inference and forecasting in continuously invertible volatility models," MPRA Paper 31767, University Library of Munich, Germany.
  22. Allen, David & Chan, Felix & McAleer, Michael & Peiris, Shelton, 2008. "Finite sample properties of the QMLE for the Log-ACD model: Application to Australian stocks," Journal of Econometrics, Elsevier, vol. 147(1), pages 163-185, November.
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