This paper is a study of continuous–time singular spectrum analysis (SSA). We show that the principal eigenfunctions are solutions to a set of linear ordinary differential equations (ODEs) with constant coefficients. We also introduce a natural generalization of SSA, based on using local (Lie–) transformation groups to construct the trajectory function. The time translations (delay coordinates) used in standard SSA is a special case. A general relation between the transformation group used in the construction of the trajectory matrix and the principal eigenfunctions is demonstrated. The eigenfunctions satisfy a simple type of linear ODE with time–dependent coefficient, determined by the infinitesimal generator of the transformation group. Finally, more general one–parameter mappings are considered.