Singular Spectrum Analysis is now a well known, almost classical method, which has found much application for time series analysis. In this paper, we consider multivariate singular spectrum analysis (MSSA) from the theoretical point of view. We assess the behavior of the trajectory matrix, which is the result of the first step of MSSA and further steps depends on its structure and characteristics, with respect to different values of the MSSA parameters. Several forms of this matrix will be considered and their performances for the analysis and forecasting time series data are evaluated. Additionally, the optimality of the MSSA parameters are considered and various bounds are introduced.
