Certain ”spurious long memory” processes mimic the behavior of fractional integration in that the variance of their sample mean behaves like that of a fractionally integrated process of some order D. We show, however, experimentally that a fractional integration test may discriminate between spurious long memory of order D and integration of order D. Further, we suggest a test for the null hypothesis that the order of integration does not change from one subperiod to another. It simply builds on the difference of the estimates from the respective subsamples that are split exogenously. Upon appropriate normalization a limiting standard normal distribution arises. With these methods we tackle the question whether international and sectoral bank equity index returns are fractionally integrated and whether the memory parameters have changed. The daily data are split into three regimes: one pre-crises subsample, a second including the collapse of the Lehman Brothers bank, and a third covering the Euro area sovereign debt crisis. In particular, we provide evidence that both turmoils had differing international effects.