This paper uses a decomposition of the data into common and idiosyncratic components to develop procedures that test if these components satisfy the null hypothesis of stationarity. The decomposition also allows us to construct pooled tests that satisfy the cross-section independence assumption. In simulations, tests on the components separately generally have better properties than testing the observed series. However, the results are less than satisfactory, especially in comparison with similar procedures developed for unit root tests. The problem can be traced to the properties of the stationarity test, and is not due to the weakness of the common-idiosyncratic decomposition. We apply both panel stationarity and unit root tests to real exchange rates. We found evidence in support of a large stationary common factor. Rejections of PPP are likely due to non-stationarity of country-specific variations.