The different forms of the multivariate singular spectrum analysis (SSA) and their associated forecasting algorithms are considered from both theoretical and practical points of view. The new multivariate vector forecasting algorithm is introduced and its uniqueness is evaluated. The performance of the new multivariate forecasting algorithm is assessed against the existent multivariate technique using various simulated and real data sets (namely European Electricity and Gas series). The forecasting results confirm that the performance of the new multivariate approach is more accurate than the current approach. The optimality of the window length and the number of eigenvalues in multivariate SSA are considered and various bounds are recommended. The effect of common components between two time series is evaluated through a simulation study. The concept of similarity and dissimilarity are also considered based on the matched components among series.
