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Linear and nonlinear regression with stable errors

Author

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  • Nolan, John P.
  • Ojeda-Revah, Diana

Abstract

In this paper we describe methods and evaluate programs for linear regression by maximum likelihood when the errors have a heavy tailed stable distribution. The asymptotic Fisher information matrix for both the regression coefficients and the error distribution parameters are derived, giving large sample confidence intervals for all parameters. Simulated examples are shown where the errors are stably distributed and also where the errors are heavy tailed but are not stable, as well as a real example using financial data. The results are then extended to nonlinear models and to non-homogeneous error terms.

Suggested Citation

  • Nolan, John P. & Ojeda-Revah, Diana, 2013. "Linear and nonlinear regression with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 186-194.
  • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:186-194
    DOI: 10.1016/j.jeconom.2012.08.008
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    References listed on IDEAS

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    1. Marc Hallin & Yves-Caoimhin Swan & Thomas Verdebout & David Veredas, 2013. "R-estimation in linear models with stable errors," ULB Institutional Repository 2013/136281, ULB -- Universite Libre de Bruxelles.
    2. repec:wsi:wschap:9789814287067_0001 is not listed on IDEAS
    3. 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..
    4. 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.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    6. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    7. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
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    Cited by:

    1. repec:spr:comgts:v:14:y:2017:i:4:d:10.1007_s10287-017-0282-9 is not listed on IDEAS
    2. repec:gam:jrisks:v:6:y:2018:i:3:p:93-:d:168825 is not listed on IDEAS
    3. Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    4. Lorenzo Ricci & Vincenzo Verardi & Catherine Vermandele, 2016. "A Highly Efficient Regression Estimator for Skewed and/or Heavy-tailed Distributed Errors," Working Papers 19, European Stability Mechanism.
    5. repec:gam:jecnmx:v:4:y:2016:i:2:p:25:d:69492 is not listed on IDEAS
    6. 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.
    7. Sio Chong U & Jacky So & Deng Ding & Lihong Liu, 2016. "An efficient Fourier expansion method for the calculation of value-at-risk: Contributions of extra-ordinary risks," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-27, March.

    More about this item

    Keywords

    Heavy tailed regression; Stable distributions; Score function;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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