In this paper we use fractional integration techniques to examine the degree of integration of four US stock market indices, namely the Standard and Poor, Dow Jones, Nasdaq and NYSE, at a daily frequency from January 2005 till December 2009. We analyse the weekly structure of the series and investigate their characteristics depending on the specific day of the week. The results indicate that the four series are highly persistent; a small degree of mean reversion (i.e., orders of integration strictly smaller than 1) is found in some cases for S&P and the Dow Jones indices. The most interesting findings are the differences in the degree of dependence for different days of the week. Specifically, lower orders of integration are systematically observed for Mondays and Fridays, consistently with the day of the week effect frequently found in financial data.