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GARCH models without positivity constraints: Exponential or Log GARCH?

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

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 particular EGARCH models, and under much stronger assumptions. The comparison is pursued via simulation experiments and estimation on real data.

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Bibliographic Info

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
Date of revision:
Publication status: Published in Journal of Econometrics, 2013, Vol. 177, no. 1. pp. 34-46.Length: 12 pages
Handle: RePEc:dau:papers:123456789/10571

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Related research

Keywords: Tail index; Strict stationarity; Quasi-Maximum Likelihood; log-GARCH; EGARCH;

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References

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  1. Genaro Sucarrat & Alvaro Escribano, 2010. "The power log-GARCH model," Economics Working Papers we1013, Universidad Carlos III, Departamento de Economía.
  2. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper, Tilburg University, Center for Economic Research 1992-40, Tilburg University, Center for Economic Research.
  3. 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.
  4. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
  5. Christian Francq & Jean-Michel Zakoïan, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Post-Print, HAL hal-00732536, HAL.
  6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
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  9. 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, Elsevier, vol. 147(1), pages 163-185, November.
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  11. BAUWENS, Luc & GIOT, Pierre, . "The logarithmic ACD model: an application to the bid-ask quote process of three NYSE stocks," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1497, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  14. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 115-127.
  15. Kristensen Dennis & Rahbek Anders, 2009. "Asymptotics of the QMLE for Non-Linear ARCH Models," Journal of Time Series Econometrics, De Gruyter, 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.
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Citations

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Cited by:
  1. Chen, Min & Zhu, Ke, 2013. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," MPRA Paper 50487, University Library of Munich, Germany.
  2. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effect in Financial Returns," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 14022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Sucarrat, Genaro & Escribano, Alvaro, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," MPRA Paper 50699, University Library of Munich, Germany.
  4. Wintenberger, Olivier, 2013. "Continuous invertibility and stable QML estimation of the EGARCH(1,1) model," MPRA Paper 46027, University Library of Munich, Germany.
  5. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
  6. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2013. "Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown," MPRA Paper 49344, University Library of Munich, Germany.
  7. Francq, Christian & Sucarrat, Genaro, 2013. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," MPRA Paper 51783, University Library of Munich, Germany.

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