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Asymptotics of the QMLE for Non-Linear ARCH Models

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Author Info

  • Kristensen Dennis

    (Columbia University)

  • Rahbek Anders

    (University of Copenhagen)

Abstract

Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -- including for example Asymmetric Power ARCH and log-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance function has a finite log-moment, and finite second moment of the rescaled error. Asymptotic normality of the estimator is established under the additional assumption that certain ratios involving the conditional variance function are suitably bounded, and that the rescaled errors have little more than fourth moment. We verify our general conditions, including identification, for a wide range of leading specific ARCH models.

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Bibliographic Info

Article provided by De Gruyter in its journal Journal of Time Series Econometrics.

Volume (Year): 1 (2009)
Issue (Month): 1 (April)
Pages: 1-38

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Handle: RePEc:bpj:jtsmet:v:1:y:2009:i:1:n:2

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Cited by:
  1. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
  2. Mika Meitz & Pentti Saikkonen, 2008. "Parameter Estimation in Nonlinear AR-GARCH Models," Economics Working Papers ECO2008/25, European University Institute.
  3. Peter Reinhard Hansen & Zhuo Huang, 2012. "Exponential GARCH Modeling with Realized Measures of Volatility," CREATES Research Papers 2012-44, School of Economics and Management, University of Aarhus.
  4. 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.
  5. Kristensen, Dennis & Rahbek, Anders, 2010. "Likelihood-based inference for cointegration with nonlinear error-correction," Journal of Econometrics, Elsevier, vol. 158(1), pages 78-94, September.
  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. Kurt Brannas & Albina Soultanaeva, 2011. "Influence of news from Moscow and New York on returns and risks of Baltic States’ stock markets," Baltic Journal of Economics, Baltic International Centre for Economic Policy Studies, vol. 11(1), pages 109-124, July.

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