@techreport{Loretan2007note,
abstract = {Since Mandelbrot's seminal work (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 regression models with infinite-variance variables. These properties differ in several important aspects from those in the well-known finite variance case. In the infinite-variance case when the regressor and error term share the same index of stability, the coefficient of determination has a nondegenerate asymptotic distribution on the entire [0,1] interval, and the probability density function of this distribution is unbounded at 0 and 1. We provide closedform expressions for the cumulative distribution function and probability density function of this limit random variable. 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 asymptotically.},
author = {Michael Stanislaus Loretan and Jeong-Ryeol Kurz-Kim},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C13; C21; G12; C12; 330; Regression models; alpha-stable distributions; infinite variance; coefficient of determination; Fama-MacBeth regression; Monte Carlo simulation; Regression; Sch\"{a}tztheorie; Statistische Verteilung; Capital Asset Pricing Model; Theorie},
language = {eng},
number = {2007,10},
title = {A note on the coefficient of determination in regression models with infinite-variance variables},
type = {Discussion paper Series 1 / Volkswirtschaftliches Forschungszentrum der Deutschen Bundesbank},
url = {http://hdl.handle.net/10419/19687},
year = {2007}
}