The non-stationarity of many macroeconomic time-series has lead to an increased demand for economic models that are able to generate fragile equilibria. For instance, the natural unemployment rate is allowed to shift over time depending on past unemployment. Actually, many European unemployment series seem to exhibit a unit root or persistence. This view is questioned in the paper using German data on unemployment. A new class of time-series models, the fractionally integrated ARMA model, that allows the difference parameter to take real values, enables the researcher to separate long memory and short memory in the data. It is shown that using this approach the unit root hypothesis is rejected but unemployment exhibits long memory.