we investigate the collinearity of vector time series in the frequency domain, by examining the rank of the spectral density matrix at a given frequency of interest. rank reduction corresponds to collinearity at the given frequency. when the time series data is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. we pursue a full understanding of rank through the schur complements of the spectral density matrix, and test for rank reduction via assessing the positivity of these schur complements, which are obtained from a nonparametric estimator of the spectral density. we provide new asymptotic results for the schur complements, under the fixed bandwidth ratio paradigm. the test statistics are $o_p (1)$ under the alternative, but under the null hypothesis of collinearity the test statistics are $o_p (t^{-1})$, and the limiting distribution is non-standard. subsampling is used to obtain the limiting null quantiles. simulation study and an empirical illustration for six-variate time series data are provided.