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Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case

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  • Søren Tolver Jensen
  • Anders Rahbek

Abstract

We establish consistency and asymptotic normality of the quasi-maximum likelihood estimator in the linear ARCH model. Contrary to the existing literature, we allow the parameters to be in the region where no stationary version of the process exists. This implies that the estimator is always asymptotically normal. Copyright The Econometric Society 2004.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00504.x
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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 72 (2004)
Issue (Month): 2 (03)
Pages: 641-646

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Handle: RePEc:ecm:emetrp:v:72:y:2004:i:2:p:641-646

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Cited by:
  1. Erie Febrian & Aldrin Herwany, 2010. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Business, Management and Finance 201005, Department of Management and Business, Padjadjaran University, revised May 2010.
  2. Guglielmo Maria Caporale & Christos Ntantamis & Theologos Pantelidis & Nikitas Pittis, 2004. "The Bds Test As A Test For The Adequacy Of A Garch(1,1) Specification: A Monte Carlo Study," Public Policy Discussion Papers 04-14, Economics and Finance Section, School of Social Sciences, Brunel University.
  3. Tamara Burdisso & Eduardo Ariel Corso, 2011. "Uncertainty and Portfolio Dollarization. The Argentine Case in the Last Half Century," Ensayos Económicos, Central Bank of Argentina, Economic Research Department, vol. 1(63), pages 41-95, July - Se.
  4. Peter Reinhard Hansen & Zhuo Huang, 2012. "Exponential GARCH Modeling with Realized Measures of Volatility," Economics Working Papers ECO2012/26, European University Institute.
  5. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
  6. Aknouche, Abdelhakim & Al-Eid, Eid M. & Hmeid, Aboubakry M., 2011. "Offline and online weighted least squares estimation of nonstationary power ARCH processes," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1535-1540, October.
  7. Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, School of Economics and Management, University of Aarhus.
  8. Christensen, Bent Jesper & Dahl, Christian M. & Iglesias, Emma M., 2012. "Semiparametric inference in a GARCH-in-mean model," Journal of Econometrics, Elsevier, vol. 167(2), pages 458-472.
  9. Francq, Christian & Zakoian, Jean-Michel, 2010. "Strict stationarity testing and estimation of explosive ARCH models," MPRA Paper 22414, University Library of Munich, Germany.
  10. Emma Iglesias & Jean Marie Dufour, 2004. "Finite Sample and Optimal Inference in Possibly Nonstationary ARCH Models with Gaussian and Heavy-Tailed Errors," Econometric Society 2004 North American Summer Meetings 161, Econometric Society.
  11. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
  12. Erie Febrian & Aldrin Herwany, 2009. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Economics and Development Studies (WoPEDS) 200911, Department of Economics, Padjadjaran University, revised Sep 2009.
  13. Han, Heejoon & Park, Joon Y., 2012. "ARCH/GARCH with persistent covariate: Asymptotic theory of MLE," Journal of Econometrics, Elsevier, vol. 167(1), pages 95-112.
  14. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, . "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, School of Economics and Management, University of Aarhus.
  15. Westerlund, Joakim, 2014. "On the choice of test for a unit root when the errors are conditionally heteroskedastic," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 40-53.

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