Spectral approach to parameter-free unit root testing

A relatively simple frequency-type testing procedure for unit root potentially contaminated by an additive stationary noise is introduced, which encompasses general settings and allows for linear trends. The proposed test for unit root versus stationarity is based on a finite number of periodograms computed at low Fourier frequencies. It is not sensitive to the selection of tuning parameters defining the range of frequencies so long as they are in the vicinity of zero. The test does not require augmentation, has parameter-free non-standard asymptotic distribution and is correctly sized. The consistency rate under the alternative of stationarity reveals the relation between the power of the test and the long-run variance of the process. The finite sample performance of the test is explored in a Monte Carlo simulation study, and its empirical application suggests rejection of the unit root hypothesis for some of the Nelson-Plosser time series.