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R-estimators in GARCH models: asymptotics and applications

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  • Hang Liu
  • Kanchan Mukherjee

Abstract

SummaryThe quasi-maximum likelihood estimation is a commonly-used method for estimating the generalized autoregressive conditional heteroscedastic parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the underlying error distribution. In this paper, we propose a novel class of estimators of the generalized autoregressive conditional heteroscedastic parameters based on ranks of the residuals, called R-estimators, with the property that they are asymptotically normal under the existence of a finitemoment of the errors and are highly efficient. We propose a fast algorithm for computing the R-estimators. Both real data analysis and simulations show the superior performance of the proposed estimators under the heavy-tailed and asymmetric distributions.

Suggested Citation

  • Hang Liu & Kanchan Mukherjee, 2022. "R-estimators in GARCH models: asymptotics and applications," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 98-113.
    • Handle: RePEc:oup:emjrnl:v:25:y:2022:i:1:p:98-113.
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    References listed on IDEAS

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    1. Arie Preminger & Giuseppe Storti, 2017. "Least‐squares estimation of GARCH(1,1) models with heavy‐tailed errors," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 221-258, June.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Francq, Christian & Lepage, Guillaume & Zakoïan, Jean-Michel, 2011. "Two-stage non Gaussian QML estimation of GARCH models and testing the efficiency of the Gaussian QMLE," Journal of Econometrics, Elsevier, vol. 165(2), pages 246-257.
    4. Mukherjee, Kanchan & Bai, Z. D., 2002. "R-estimation in Autoregression with Square-Integrable Score Function," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 167-186, April.
    5. Mukherjee, Kanchan, 2007. "Generalized R-estimators under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 141(2), pages 383-415, December.
    6. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.
    7. Mukherjee, Kanchan, 2008. "M-Estimation In Garch Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1530-1553, December.
    8. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    9. Andrews, Beth, 2012. "Rank-Based Estimation For Garch Processes," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1037-1064, October.
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