Before revision: We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) , a non-parametric automated technique to extract signals at different frequencies. It is useful to uncover co-movements per frequency, understand their commonalities and specificities, and also the relative cyclical position of the signals .
After revision: We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) , a non-parametric and can be applied to series not on phase, highly nonlinear and modulated both in frequency and amplitude. We prove a uniqueness theorem that in case of common information and without the need of fitting a factor model, allows us to identify common sources of variation .