A note on the coefficient of determination in models with infinite variance variables
By: Jeong-Ryeol Kurz-Kim and Mico Loretan
Contributors: Loretan, Mico
Series: International finance discussion papers -- no. 895; International finance discussion papers (Online) -- no. 895.
Publisher: Federal Reserve Board
Published: 2007
Place of publication: Washington, D.C
Language: eng
Format: [electronic resource] /
Description: "Since the seminal work of Mandelbrot (1963), alpha-stable distributions with infinite variance have been regarded as a more realistic distributional assumption than the normal distribution for some economic variables, especially financial data.  After providing a brief survey of theoretical results on estimation and hypothesis testing in regression models with infinite-variance variables, we examine the statistical properties of the coefficient of determination in models with alpha-stable variables.  If the regressor and error term share the same index of stability alpha<2, the coefficient of determination has a nondegenerate asymptotic distribution on the entire [0, 1] interval, and the density of this distribution is unbounded at 0 and 1.  We provide closed-form expressions for the cumulative distribution function and probability density function of this limit random variable.  In contrast, if the indices of stability of the regressor and error term are unequal, the coefficient of determination converges in probability to either 0 or 1, depending on which variable has the smaller index of stability.  In an empirical application, we revisit the Fama-MacBeth two-stage regression and show that in the infinite-variance case the coefficient of determination of the second-stage regression converges to zero in probability even if the slope coefficient is nonzero"--Federal Reserve Board web site.
Notes: Title from PDF file as viewed on 7/23/2007.

Includes bibliographical references.

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