We analyse the time series properties of the S&P500 dividend--price ratio in the light of long-memory, structural breaks and rational bubbles. We find an increase in the long-memory parameter in the early 1990s by applying a test recently proposed by Sibbertsen and Kruse [<italic>J. Time Series Anal.</italic>, 2009, <bold>30</bold>, 263--285]. An application of the unit root test against long memory of Demetrescu <italic>et al.</italic> [<italic>Econometr. Theory</italic>, 2008, <bold>24</bold>, 176--215] suggests that the pre-break data can be characterized by long memory, while the post-break sample contains a unit root. These results reconcile two empirical findings that are seen as contradictory: on the one hand, they confirm the existence of fractional integration in the S&P500 log-dividend--price ratio and, on the other, they are consistent with the existence of a rational bubble. The result of a changing memory parameter in the dividend--price ratio has an important implication for the literature on return predictability: the shift from a stationary dividend--price ratio to a unit root process in 1991 is likely to have caused the well-documented failure of conventional return prediction models since the 1990s.
