TAIL DEPENDENCE OF OLS

This paper shows that if the errors in a multiple regression model are heavy-tailed, the ordinary least squares (OLS) estimators for the regression coefficients are tail-dependent. The tail dependence arises, because the OLS estimators are stochastic linear combinations of heavy-tailed random variables. Moreover, tail dependence also exists between the fitted sum of squares (FSS) and the residual sum of squares (RSS), because they are stochastic quadratic combinations of heavy-tailed random variables.