Spectral regression is considered for cointegrated time series with long memory innovations. The estimates we advocate are shown to be consistent when cointegrating relationships among stationary processes are investigated, while OLS are innsistent due to correlation between the regressor and the cointegrating residuals; in the presence of unit roots, these estimates share the same asymptotic distribution as OLS. As a corollary of the main result, we provide a funcional central limit theorem for quadratic forms in nostationary fractionally integrated processe