Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density

A nonparametric procedure for identifying the differencing operator of a non-stationary time series is presented and tested. Any proposed differencing operator is first applied to the time series, and the spectral density is tested for zeroes corresponding to the polynomial roots of the operator. A nonparametric tapered spectral density estimator is used, and the subsampling methodology is applied to obtain critical values. Simulations explore the effectiveness of the procedure under a variety of scenarios involving non-stationary processes.