A NONPARAMETRIC TEST FOR I(0)

There is frequently interest in testing that a scalar or vector time s eries 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 fr actional alternatives. The test is nonparametric, and indeed makes no assumptions on spectral behaviour away from zero frequency. It seems l ikely to have good efficiency against fractional alternatives, relativ e to other nonparametric tests. The test is given large sample justifi cation, subjected to a Monte Carlo analysis of finite sample behaviour , and applied to various empirical data series.