Bootstrapping Fuzzy-GARCH Regressions on the Day of the Week Effect in Stock Returns: Applications in MATLAB

Abstract

This paper examines the well know day of the week effect on stock returns. Various approaches have been developed and applied in order to examine calendar effects in stock returns and to formulate appropriate financial and risk portfolios. We propose an alternative approach in the estimation of the day of the week effect. More specifically we apply fuzzy regressions with triangular membership function in four major stock market index returns. We expect that if the day of the week is valid, then the Monday returns should be negative or lower than the other days of the week and in addition Friday returns should be the highest. The main findings and results are mixed and based on the fuzzy regression we conclude that there isn’t the day of the week or the Monday effect. Specifically, we find a reverse Monday effect in S&P 500, a negative Friday effect in FTSE-100, a positive Tuesday effect in NIKKEI-225 and no effects in DAX index. The specific approach is appropriate as fuzzy logic regression is appropriate and able to capture the impressions and nonlinearities in finance and human behaviour, which are main characteristics in financial industry. Furthermore fuzzy regression avoids the classification of dummy variables to values of one and zero, as we do in the traditional statistical and econometric methodology