This papers finds evidence of fractional integration for a number of monthly ex post real interest rate series using the GPH semiparametric estimator on data from fourteen European countries and the US. However, we pose empirical questions on certain time series requirements that emerge from fractional integration and we find that they do not hold pointing to "spurious" long memory and casting doubts with respect to the theoretical origins of long memory in our sample. Common stochastic trends expressed as the sum of stationary past errors do not seem appropriate as an explanation of real interest rate covariation. From an economic perspective, our results suggest that most European countries show higher speed of real interest rate equalization with Germany rather than the US.