Salient features of dependence in daily US stock market indices

•In general, we observe a slight decrease in the degree of dependence across the years in the sample.•The results suggest the presence of one structural break in the series related with the stock market crash in October 1987.•With respect to the volatility processes, there is strong evidence of some degree of stationary long memory.

This paper deals with the analysis of long range dependence in the US stock market. We focus first on the log-values of the Dow Jones Industrial Average, Standard and Poors 500 and Nasdaq indices, daily from February, 1971 to February, 2007. The volatility processes are examined based on the squared and the absolute values of the returns series, and the stability of the parameters across time is also investigated in both the level and the volatility processes. A method that permits us to estimate fractional differencing parameters in the context of structural breaks is conducted in this paper. Finally, the “day of the week” effect is examined by looking at the order of integration for each day of the week, providing also a new modeling approach to describe the dependence in this context.