Maximum Likelihood Estimates of Regression Coefficients with alpha-stable residuals and Day of Week effects in Total Returns on Equity Indices

This Paper summarizes the theory of Maximum Likelihood Estimation of regressions with alpha-stable residuals. Day of week effects in returns on equity indices, adjusted for dividends (total returns) are estimated and tested using this and traditional OLS methodology. I find that the alpha-stable methodology is feasible. There are some differences in the results from the two methodologies. The conclusion remains that if individual coefficients are of interest and the residuals have fat tails and a possible alpha-stable distribution, the results can be checked for robustness using methods such as those employed here.