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

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Author Info
Kurz-Kim, Jeong-Ryeol
Loretan, Michael Stanislaus
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.

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Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2007,10.

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Date of creation: 2007
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Handle: RePEc:zbw:bubdp1:5574

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Keywords: Regression models alpha-stable distributions infinite variance coefficient of determination Fama-MacBeth regression Monte Carlo simulation

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  1. repec:rus:hseeco:318682 is not listed on IDEAS
  2. Reitz, Stefan & Schmidt, Markus & Taylor, Mark P., 2007. "End-user order flow and exchange rate dynamics," Discussion Paper Series 1: Economic Studies 2007,05, Deutsche Bundesbank, Research Centre. [Downloadable!]
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