Linear and nonlinear regression with stable errors
AbstractIn 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 172 (2013)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/jeconom
Heavy tailed regression; Stable distributions; Score function;
Find related papers by 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- 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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- 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.
- 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.
- Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
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