Multivariate Circulant Singular Spectrum Analysis ∗ JuanB´ogalo Universidad Aut´onoma de Madrid SPAIN Pilar Poncela Universidad Aut´onoma de Madrid SPAIN Eva Senra Universidad de Alcal´a SPAIN December 2, 2021 Abstract Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) is a non-parametric automated technique that allows to extract signals of time series at any frequency specified beforehand. It is useful to uncover co-movements at different frequencies and understand their commonalities and specificities. We apply M-CiSSA to understand the main drivers and co-movements of energy commodity prices at trend and cyclical frequencies that are key to assess energy policy at different time horizons. We clearly distinguish the detached behaviour of US natural gas from the rest of energy commodities at both frequencies while coals and Japan natural gas only decouple at the cyclical frequency. Keywords: Block circulant matrices, multivariate signal extraction, singular spectrum analysis, co-movement, decoupled markets, energy prices * Financial support from the Spanish government, contract grants MINECO/FEDER ECO2015-70331-C2-1-R, ECO2015-66593-P, ECO2016-76818-C3-3-P, PID2019-107161GB-C32 and PID2019-108079GB-C22 is acknowledged. 1 arXiv:2007.07561v1 [eess.SP] 15 Jul 2020