Understanding fluctuations through Multivariate Circulant Singular Spectrum Analysis

We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) to provide a comprehensive framework to analyze fluctuations, extracting the underlying components of a set of time series, disentangling their sources of variation and assessing their relative phase or cyclical position at each frequency. Our novel method is non-parametric and can be applied to series out of phase, highly nonlinear and modulated both in frequency and amplitude. We prove a uniqueness theorem that in the case of common information and without the need of fitting a factor model, allows us to identify common sources of variation. This technique can be quite useful in several fields such as climatology, biometrics, engineering or economics among others. We show the performance of M-CiSSA through a synthetic example of latent signals modulated both in amplitude and frequency and through the real data analysis of energy prices to understand the main drivers and co-movements of primary energy commodity prices at various frequencies that are key to assess energy policy at different time horizons.