  Dimension reduction techniques for multivariate time series decompose the
observed series into a few useful independent/orthogonal univariate components.
We develop a spectral domain method for multivariate second-order stationary
time series that linearly transforms the observed series into several groups of
lower-dimensional multivariate subseries. These multivariate subseries have
non-zero spectral coherence among components within a group but have zero
spectral coherence among components across groups. The observed series is
expressed as a sum of frequency components whose variances are proportional to
the spectral matrices at the respective frequencies. The demixing matrix is
then estimated using an eigendecomposition on the sum of the variance matrices
of these frequency components and its asymptotic properties are derived.
Finally, a consistent test on the cross-spectrum of pairs of components is used
to find the desired segmentation into the lower-dimensional subseries. The
numerical performance of the proposed method is illustrated through simulation
examples and an application to modeling and forecasting wind data is presented.
