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One-step R-estimation in linear models with stable errors

Author

Listed:
  • Hallin, Marc
  • Swan, Yvik
  • Verdebout, Thomas
  • Veredas, David

Abstract

Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step R-estimation method and investigate its asymptotic performances under stable densities. Contrary to traditional least squares, the proposed R-estimators remain root-n consistent (the optimal rate) under the whole family of stable distributions, irrespective of their asymmetry and tail index. While parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (α0,b0) of the tail index α and skewness parameter b, while preserving root-n consistency under any (α,b) as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.

Suggested Citation

  • Hallin, Marc & Swan, Yvik & Verdebout, Thomas & Veredas, David, 2013. "One-step R-estimation in linear models with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 195-204.
  • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:195-204
    DOI: 10.1016/j.jeconom.2012.08.016
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    References listed on IDEAS

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    1. Bantli, Faouzi El & Hallin, Marc, 1999. "L1-estimation in linear models with heterogeneous white noise," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 305-315, December.
    2. Robert Blattberg & Thomas Sargent, 2010. "Regression With Non-Gaussian Stable Disturbances: Some Sampling Results," World Scientific Book Chapters,in: Perspectives On Promotion And Database Marketing The Collected Works of Robert C Blattberg, chapter 1, pages 7-16 World Scientific Publishing Co. Pte. Ltd..
    3. Knight, Keith, 1998. "Bootstrapping sample quantiles in non-regular cases," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 259-267, March.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, Fall.
    5. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    6. Marc Hallin & Yvik Swan & Thomas Verdebout & David Veredas, 2011. "Rank-based testing in linear models with stable errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 305-320.
    7. Deo, Rohit S., 2002. "On testing the adequacy of stable processes under conditional heteroscedasticity," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 257-270, March.
    8. Allal, Jelloul & Kaaouachi, Abdelali & Paindaveine, Davy, 2001. "R-estimation for ARMA models," MPRA Paper 21167, University Library of Munich, Germany.
    9. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
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    Citations

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    Cited by:

    1. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    2. Tsionas, Mike G., 2016. "Bayesian analysis of multivariate stable distributions using one-dimensional projections," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 185-193.
    3. repec:gam:jecnmx:v:4:y:2016:i:2:p:25:d:69492 is not listed on IDEAS
    4. Nolan, John P. & Ojeda-Revah, Diana, 2013. "Linear and nonlinear regression with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 186-194.
    5. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-28, May.
    6. Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    7. 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.
    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. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute for the Study of Labor (IZA).

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