This paper uses the tests of Robinson (1994a) to analyse the degree of dependence in the intertemporal structure of daily stock returns in the S&P500 index. These tests have a standard null limit distribution and are the most efficient ones when carried out against the appropriate alternatives. In addition, they allow one to incorporate the Bloomfield (1973) exponential spectral model for the underlying I(0) disturbances. The full sample, which comprises 17,000 observations, is first divided in 10 subsamples of 1700 observations each. These are then grouped two by two, and five by five; finally, the whole sample is considered. The results indicate that the degree of dependence remains relatively constant over time, with the order of integration of stock returns fluctuating slightly above or below zero. On the whole, there is very little evidence of fractional integration