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Discussion Paper Series 1: Economic Studies, Deutsche Bundesbank >
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http://hdl.handle.net/10419/19687
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| Title: | | A note on the coefficient of determination in regression models with infinite-variance variables  |
| Authors: | | Loretan, Michael Stanislaus Kurz-Kim, Jeong-Ryeol |
| Issue Date: | | 2007 |
| Series/Report no.: | | Discussion paper Series 1 / Volkswirtschaftliches Forschungszentrum der Deutschen Bundesbank 2007,10 |
| 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. |
| Subjects: | | Regression models alpha-stable distributions infinite variance coefficient of determination Fama-MacBeth regression Monte Carlo simulation |
| JEL: | | C13 C21 G12 C12 |
| Document Type: | | Working Paper |
| Appears in Collections: | | Discussion Paper Series 1: Economic Studies, Deutsche Bundesbank
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