There is frequently interest in testing that a scalar or vector time series is I(0), possibly after first- differencing or other detrending, while the I(0) assumption is also taken for granted in autocorrelation-consistent variance estimation. We propose a test for I(0) against fractional alternatives. The test is non-parametric, and indeed makes no assumptions on spectral behaviour away from zero frequency. It seems likely to have good efficiency against fractional alternatives, relative to other nonparametric tests. The test is given large samle justification, subjected to a Monte Carlo analysis of finite sample behaviour, and applied to various empirical data series.