A Note on the Coefficient of Determination in Models with Infinite Variance Variables

Abstract

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