Principal component analysis using frequency components of multivariate time series

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