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Rank-Based Estimation For Garch Processes

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  • Andrews, Beth

Abstract

We consider a rank-based technique for estimating generalized autoregressive conditionally heteroskedastic (GARCH) model parameters, some of which are scale transformations of conventional GARCH parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given in Jaeckel (1972, Annals of Mathematical Statistics 43, 1449–1458). They are useful for GARCH order selection and preliminary estimation. We give a limiting distribution for the rank estimators that holds when the true parameter vector is in the interior of its parameter space and when some GARCH parameters are zero. The limiting theory is used to show that the rank estimators are robust, can have the same asymptotic efficiency as maximum likelihood estimators, and are relatively efficient compared to traditional Gaussian and Laplace quasi-maximum likelihood estimators. The behavior of the estimators for finite samples is studied via simulation, and we use rank estimation to fit a GARCH model to exchange rate log-returns.

Suggested Citation

  • Andrews, Beth, 2012. "Rank-Based Estimation For Garch Processes," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1037-1064, October.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:05:p:1037-1064_00
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    Cited by:

    1. Ke Zhu & Wai Keung Li, 2015. "A New Pearson-Type QMLE for Conditionally Heteroscedastic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 552-565, October.
    2. Marc Hallin & Davide La Vecchia, 2017. "A Simple R-Estimation Method for Semiparametric Duration Models," Working Papers ECARES ECARES 2017-01, ULB -- Universite Libre de Bruxelles.
    3. Marc Hallin & Davide La Vecchia, 2014. "Semiparametrically Efficient R-Estimation for Dynamic Location-Scale Models," Working Papers ECARES ECARES 2014-45, ULB -- Universite Libre de Bruxelles.
    4. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    5. Preminger, Arie & Storti, Giuseppe, 2014. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," MPRA Paper 59082, University Library of Munich, Germany.

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