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Garch models without positivity constraints: exponential or log garch?

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

This paper studies the probabilistic properties and the estimation of the asymmetric log-GARCH($p,q$) model. In this model, the log-volatility is written as a linear function of past values of the log-squared observations, with coefficients depending on the sign of the observations, and past log-volatility values. Conditions are obtained for the existence of solutions and finiteness of their log-moments. We also study the tail properties of the solution. Under mild assumptions, we show that the quasi-maximum likelihood estimation of the parameters is strongly consistent and asymptotically normal. Simulations illustrating the theoretical results and an application to real financial data are proposed.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41373.

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Date of creation: 16 Sep 2012
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Handle: RePEc:pra:mprapa:41373
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  1. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
  2. He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
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  4. BAUWENS, Luc & GALLI, Fausto & GIOT, Pierre, 2003. "The moments of Log-ACD models," CORE Discussion Papers 2003011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Shiqing Ling & Michael McAleer, 2001. "Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models," ISER Discussion Paper 0534, Institute of Social and Economic Research, Osaka University.
  6. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  7. 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.
  8. BAUWENS, Luc & GIOT, Pierre & GRAMMIG, Joachim & VEREDAS, David, . "A comparison of financial duration models via density forecasts," CORE Discussion Papers RP 1746, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Wintenberger, Olivier & Cai, Sixiang, 2011. "Parametric inference and forecasting in continuously invertible volatility models," MPRA Paper 31767, University Library of Munich, Germany.
  10. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. 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.
  13. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  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. 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).
  16. Sucarrat, Genaro & Escribano, Álvaro, 2010. "The power log-GARCH model," UC3M Working papers. Economics we1013, Universidad Carlos III de Madrid. Departamento de Economía.
  17. Francq, Christian & Zakoïan, Jean-Michel, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Journal of Econometrics, Elsevier, vol. 159(1), pages 151-165, November.
  18. 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.
  19. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  20. Wintenberger, Olivier, 2013. "Continuous invertibility and stable QML estimation of the EGARCH(1,1) model," MPRA Paper 46027, University Library of Munich, Germany.
  21. 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.
  22. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  23. repec:hal:journl:peer-00732536 is not listed on IDEAS
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