In this work, we develop multivariate functional singular spectrum analysis (MFSSA) over different dimensional domains which is the functional extension of multivariate singular spectrum analysis (MSSA). In the following, we provide all of the necessary theoretical details supporting the work as well as the implementation strategy that contains the recipes needed for the algorithm. We provide a simulation study showcasing the better performance in reconstruction accuracy of a multivariate functional time series (MFTS) signal found using MFSSA as compared to other approaches and we give a real data study showing how MFSSA enriches analysis using intraday temperature curves and remote sensing images of vegetation. MFSSA is available for use through the Rfssa R package.

28 pages for the paper, 15 pages for the supplementary material, 8 figures total