This study considers the time series behavior of the U.S. real interest rate from 1961 to 1986. We provide a statistical characterization of the series using the methodology of Hamilton (1989), by allowing three possible regimes affecting both the mean and variance of the series. The results suggest that the ex-post real interest rate is essentially random around a mean that is different for the periods 1961-1973, 1973-1980 and 1980-1986. The variance of the process is also different in these episodes being higher in both the 1973-1980 and 1980-1986 sub-periods. The inflation rate series is also analyzed using a three regime framework and again our results show interesting patterns with shifts in both mean and variance. Various model selection tests are run and both an ex-ante real interest rate and an expected inflation series are constructed. Finally, we make clear how our results can explain some recent findings in the literature.