The distance between rival nonstationary fractional processes

Asymptotic inference on nonstationary fractional time series models, including cointegrated ones, is proceeding along two routes, determined by alternative definitions of nonstationary processes. We derive bounds for the mean squared error of the difference between (possibly tapered) discrete Fourier transforms under the two regimes. We apply the results to deduce limit theory for estimates of memory parameters, including ones for cointegrating errors, with mention also of implications for estimates of cointegrating coefficients.