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Bootstrap refinements for QML estimators of the GARCH(1,1) parameters

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  • Corradi, Valentina
  • Iglesias, Emma M.

Abstract

This paper reconsiders a block bootstrap procedure for Quasi Maximum Likelihood estimation of GARCH models, based on the resampling of the likelihood function, as proposed by Gonçalves and White [2004. Maximum likelihood and the bootstrap for nonlinear dynamic models. Journal of Econometrics 119, 199-219]. First, we provide necessary conditions and sufficient conditions, in terms of moments of the innovation process, for the existence of the Edgeworth expansion of the GARCH(1,1) estimator, up to the k-th term. Second, we provide sufficient conditions for higher order refinements for equally tailed and symmetric test statistics. In particular, the bootstrap estimator based on resampling the likelihood has the same higher order improvements in terms of error in the rejection probabilities as those in Andrews [2002. Higher-order improvements of a computationally attractive k-step bootstrap for extremum estimators. Econometrica 70, 119-162].

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  • Corradi, Valentina & Iglesias, Emma M., 2008. "Bootstrap refinements for QML estimators of the GARCH(1,1) parameters," Journal of Econometrics, Elsevier, vol. 144(2), pages 500-510, June.
    • Handle: RePEc:eee:econom:v:144:y:2008:i:2:p:500-510
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    Cited by:

    1. Arvanitis Stelios & Demos Antonis, 2018. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-38, January.
    2. João Henrique G. Mazzeu & Gloria González-Rivera & Esther Ruiz & Helena Veiga, 2020. "A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 971-990, November.
    3. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    4. Corradi, Valentina & Fernandez, Andres & Swanson, Norman R., 2009. "Information in the Revision Process of Real-Time Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 455-467.
    5. Peter Malec, 2016. "A Semiparametric Intraday GARCH Model," Cambridge Working Papers in Economics 1633, Faculty of Economics, University of Cambridge.
    6. Antonis Demos & Stelios Arvanitis, 2012. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators Revised (Extended Appendix)," DEOS Working Papers 1215, Athens University of Economics and Business.
    7. Antonis Demos & Stelios Arvanitis, 2012. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Estimators (Extended Revised Appendix)," DEOS Working Papers 1230, Athens University of Economics and Business.
    8. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    9. Gonçalves Mazzeu, Joao Henrique & González-Rivera, Gloria & Ruiz Ortega, Esther & Veiga, Helena, 2016. "A Bootstrap Approach for Generalized Autocontour Testing," DES - Working Papers. Statistics and Econometrics. WS 23457, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Antonis Demos & Dimitra Kyriakopoulou, 2011. "Bias Correction of ML and QML Estimators in the EGARCH(1,1) Model," DEOS Working Papers 1108, Athens University of Economics and Business.
    11. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    12. Moon, Seongman & Velasco, Carlos, 2013. "Tests for m-dependence based on sample splitting methods," Journal of Econometrics, Elsevier, vol. 173(2), pages 143-159.
    13. Anatolyev Stanislav, 2019. "Volatility filtering in estimation of kurtosis (and variance)," Dependence Modeling, De Gruyter, vol. 7(1), pages 1-23, February.
    14. repec:aue:wpaper:1214 is not listed on IDEAS
    15. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    16. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.
    17. Alexander Heinemann, 2019. "A Bootstrap Test for the Existence of Moments for GARCH Processes," Papers 1902.01808, arXiv.org, revised Jul 2019.
    18. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    19. 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, Department of Economics and Business Economics, Aarhus University.
    20. Antonis Demos & Stelios Arvanitis, 2010. "A New Class of Indirect Estimators and Bias Correction," DEOS Working Papers 1023, Athens University of Economics and Business.
    21. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2018. "A Residual Bootstrap for Conditional Value-at-Risk," Papers 1808.09125, arXiv.org, revised Aug 2023.
    22. Shimizu Kenichi, 2013. "The bootstrap does not alwayswork for heteroscedasticmodels," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 189-204, August.
    23. Stelios Arvanitis & Antonis Demos, 2012. "Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations," DEOS Working Papers 1229, Athens University of Economics and Business, revised 24 Aug 2012.

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