Continuous invertibility and stable QML estimation of the EGARCH(1,1) model
AbstractWe introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE). We prove the strong consistency of the Quasi Maximum Likelihood Estimator (QMLE) when the optimization procedure is done on a continuously invertible domain. This approach gives for the first time the strong consistency of the QMLE used by Nelson (1991) for the EGARCH(1,1) model under explicit but non observable conditions. In practice, we propose to stabilize the QMLE by constraining the optimization procedure to an empirical continuously invertible domain. The new method, called Stable QMLE (SQMLE), is strongly consistent when the observations follow an invertible EGARCH(1,1) model. We also give the asymptotic normality of the SQMLE under additional minimal assumptions.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 46027.
Date of creation: 07 Jan 2013
Date of revision:
Invertible models; volatility models; quasi maximum likelihood; strong consistency; asymptotic normality; exponential GARCH; stochastic recurrence equation.;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-13 (All new papers)
- NEP-ECM-2013-04-13 (Econometrics)
- NEP-ETS-2013-04-13 (Econometric Time Series)
- NEP-ORE-2013-04-13 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
- Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013.
"GARCH models without positivity constraints: Exponential or log GARCH?,"
Journal of Econometrics,
Elsevier, vol. 177(1), pages 34-46.
- Zakoïan, Jean-Michel & Wintenberger, Olivier & Francq, Christian, 2013. "GARCH models without positivity constraints: Exponential or Log GARCH?," Economics Papers from University Paris Dauphine 123456789/10571, Paris Dauphine University.
- Francq, Christian & Wintenberger, Olivier & Zakoian, Jean-Michel, 2012. "Garch models without positivity constraints: exponential or log garch?," MPRA Paper 41373, University Library of Munich, Germany.
- Zaffaroni, Paolo, 2009. "Whittle estimation of EGARCH and other exponential volatility models," Journal of Econometrics, Elsevier, vol. 151(2), pages 190-200, August.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- repec:imd:wpaper:wp2010-25 is not listed on IDEAS
- 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.
- 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.
- Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
- Genaro Sucarrat & Alvaro Escribano, 2010. "The power log-GARCH model," Economics Working Papers we1013, Universidad Carlos III, Departamento de Economía.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
- Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 187-98, April.
- Shao, Qi-Man, 1993. "Complete convergence for [alpha]-mixing sequences," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 279-287, March.
- Antonis Demos & Dimitra Kyriakopoulou, 2010. "Bias Correction of ML and QML Estimators in the EGARCH(1,1) Model," DEOS Working Papers 1108, Athens University of Economics and Business.
- Elton, John H., 1990. "A multiplicative ergodic theorem for lipschitz maps," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 39-47, February.
- 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.
- 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
14022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effect in Financial Returns," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00973922, HAL.
- Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2014. "Maximum Likelihood Estimation for Generalized Autoregressive Score Models," Tinbergen Institute Discussion Papers 14-029/III, Tinbergen Institute, revised 19 Apr 2014.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.