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

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

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.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 172 (2013)
Issue (Month): 2 ()
Pages: 195-204

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Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:195-204
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
  2. repec:cup:cbooks:9780521845731 is not listed on IDEAS
  3. 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.
  4. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
  5. 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.
  6. Blattberg, Robert & Sargent, Thomas J, 1971. "Regression with Non-Gaussian Stable Disturbances: Some Sampling Results," Econometrica, Econometric Society, vol. 39(3), pages 501-10, May.
  7. 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.
  8. Marc Hallin & Yvik Swan & Thomas Verdebout & David Veredas, 2011. "Rank-based testing in linear models with stable errors," ULB Institutional Repository 2013/136196, ULB -- Universite Libre de Bruxelles.
  9. repec:cup:cbooks:9780521608275 is not listed on IDEAS
  10. Allal, Jelloul & Kaaouachi, Abdelali & Paindaveine, Davy, 2001. "R-estimation for ARMA models," MPRA Paper 21167, University Library of Munich, Germany.
  11. Knight, Keith, 1998. "Bootstrapping sample quantiles in non-regular cases," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 259-267, March.
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