Band spectrum regression for cointegrated time series with long memory innovations

Band spectrum 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 variables are investigated, while OLS are inconsistent 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 functional central limit theorem for quadratic forms in nonstationary fractionally integrated processes.