المستودع الأكاديمي جامعة المدينة

A note on the coefficient of determination in regression models with infinite-variance variables

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dc.creator Loretan, Michael Stanislaus
dc.creator Kurz-Kim, Jeong-Ryeol
dc.date 2007
dc.date.accessioned 2013-10-16T07:06:17Z
dc.date.available 2013-10-16T07:06:17Z
dc.date.issued 2013-10-16
dc.identifier http://hdl.handle.net/10419/19687
dc.identifier ppn:529232138
dc.identifier RePEc:zbw:bubdp1:5574
dc.identifier.uri http://koha.mediu.edu.my:8181/xmlui/handle/10419/19687
dc.description 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.
dc.language eng
dc.relation Discussion paper Series 1 / Volkswirtschaftliches Forschungszentrum der Deutschen Bundesbank 2007,10
dc.rights http://www.econstor.eu/dspace/Nutzungsbedingungen
dc.subject C13
dc.subject C21
dc.subject G12
dc.subject C12
dc.subject ddc:330
dc.subject Regression models
dc.subject alpha-stable distributions
dc.subject infinite variance
dc.subject coefficient of determination
dc.subject Fama-MacBeth regression
dc.subject Monte Carlo simulation
dc.subject Regression
dc.subject Schätztheorie
dc.subject Statistische Verteilung
dc.subject Capital Asset Pricing Model
dc.subject Theorie
dc.title A note on the coefficient of determination in regression models with infinite-variance variables
dc.type doc-type:workingPaper


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