Several recent papers have presented evidence from foreign exchange and other markets suggesting that the log of excess returns can be characterized as first-order integrated processes (I(1)). This contrasts sharply with the "conventional" wisdom that log prices are integrated of order one I(1) and that log returns should therefore be integrated of order zero I(0), and even more sharply with the view that past returns have no ability to predict future returns (weak market efficiency). It has been suggested that this should be interpreted as evidence of the importance of regime-switching in asset prices, since such non-linear processes can produce these results even when returns are truly I(0).

This paper suggests an alternative interpretation. We consider whether the above results can be explained away as an artifact of the estimation procedure used. At first glance, this is not a likely explanation because
- the significance level of some of the results is very high
- the methodologies vary considerably across papers, so that a problem with any one statistical test cannot account for all the results
- simulation experiments are used to check the validity of the tests

Despite this, we suggest that the above evidence of unit roots may be spurious. Our explanation relies on the presence of several factors, including
- severe size distortion in more than one statistical test
- sensitivity to the design of the simulation experiments used to validate those tests

Once these factors are taken into account, we think that the "anomaly" vanishes. We find that there is no remaining evidence of unit roots in excess returns once we account for the size distortion. We also show that the test results seem to be consistent with simple linear data generating processes -- regime-switching is not needed to account for them.