Linear and nonlinear regression with stable errors
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.
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- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- 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.
- Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
- Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
- 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.
- 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.
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