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Quasi-Maximum Likelihood Estimation Of Semi-Strong Garch Models

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  • Escanciano, Juan Carlos

Abstract

This note proves the consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the parameters of a generalized autoregressive conditional heteroskedastic (GARCH) model with martingale difference centered squared innovations. The results are obtained under mild conditions and generalize and improve those in Lee and Hansen (1994, Econometric Theory 10, 29–52) for the local QMLE in semistrong GARCH(1,1) models. In particular, no restrictions on the conditional mean are imposed. Our proofs closely follow those in Francq and Zakoïan (2004, Bernoulli 10, 605–637) for independent and identically distributed innovations.

Suggested Citation

  • Escanciano, Juan Carlos, 2009. "Quasi-Maximum Likelihood Estimation Of Semi-Strong Garch Models," Econometric Theory, Cambridge University Press, vol. 25(2), pages 561-570, April.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:02:p:561-570_09
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    Cited by:

    1. Cerovecki, Clément & Francq, Christian & Hörmann, Siegfried & Zakoïan, Jean-Michel, 2019. "Functional GARCH models: The quasi-likelihood approach and its applications," Journal of Econometrics, Elsevier, vol. 209(2), pages 353-375.
    2. Herwartz, Helmut, 2017. "Stock return prediction under GARCH — An empirical assessment," International Journal of Forecasting, Elsevier, vol. 33(3), pages 569-580.
    3. Sucarrat, Genaro, 2020. "garchx: Flexible and Robust GARCH-X Modelling," MPRA Paper 100301, University Library of Munich, Germany.
    4. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
    5. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.
    6. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    7. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    8. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.
    9. Christian Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    10. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1236-1278, December.
    11. Todd, Prono, 2009. "Simple, Skewness-Based GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 30994, University Library of Munich, Germany, revised 30 Jul 2011.
    12. Francq, Christian & Thieu, Le Quyen, 2019. "Qml Inference For Volatility Models With Covariates," Econometric Theory, Cambridge University Press, vol. 35(1), pages 37-72, February.
    13. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    14. Christian Francq & Jean-Michel Zakoïan, 2016. "Estimating multivariate volatility models equation by equation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 613-635, June.
    15. Tingguo Zheng & Han Xiao & Rong Chen, 2021. "Generalized Autoregressive Moving Average Models with GARCH Errors," Papers 2105.05532, arXiv.org.
    16. Abdelouahab Bibi, 2021. "Asymptotic properties of QMLE for seasonal threshold GARCH model with periodic coefficients," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 477-514, June.
    17. Bibi, Abdelouahab & Ghezal, Ahmed, 2017. "Asymptotic properties of QMLE for periodic asymmetric strong and semi-strong GARCH models," MPRA Paper 81126, University Library of Munich, Germany.

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