This paper studies the use of spectral regression techniques in the context of cointegrated systems of multiple time series. Several alternatives are considered including eﬀicient and band spectral methods as well as system and single equation techniques. It is shown that single equation spectral regressions suﬀer asymptotic bias and nuisance parameter problems that render these regressions impotent for inferential purposes. By contrast systems methods are shown to be covered by LAMN asymptotic theory, bringing the advantages of asymptotic media unbiasedness, scale nuisance parameters and the convenience of asymptotic chi-squared tests. System spectral methods also have advantages over full system direct maximum likelihood in that they do not require complete speciﬁcation of the error processes. Instead they oﬀer a nonparametric treatment of regression errors which avoids certain methodological problems of dynamic speciﬁcation and permits additional generality in the class of error processes.
Phillips, Peter C.B., "Spectral Regression for Cointegrated Time Series" (1988). Cowles Foundation Discussion Papers. 1115.