Modern techniques for managing multidimensional stochastic processes that reflect the dynamics of unstable environments are proactive, which refers to decision making based on forecasting the system's state vector evolution. At the same time, the dynamics of open nonlinear systems are largely determined by their chaotic nature, which leads to a violation of stationarity and ergodicity of the series of observations and, as a result, to a catastrophic decrease in the efficiency of forecasting algorithms based on traditional methods of multivariate statistical data analysis. In this article, we make an attempt to reduce the instability influence by employing singular spectrum analysis (SSA) algorithms. This technique has been employed in a wide class of applied data analysis problems formulated in terms of singular decomposition of data matrices: technologies of immunocomputing and SSA.