Singular spectrum analysis (SSA) is a relatively recent technique for time series analysis. The idea behind SSA was originally purposed as a data adaptive method for choosing an optimal embedding dimension for attractor reconstruction. Later the technique was developed as a "stand alone" time series analysis technique. During the last decade it has been very successful and has become a standard tool in many different scientific fields, such as climatic, meteorological, geophysical, and astronomical time series analysis.
At this seminar I will give an introduction to SSA and discuss typical time series for which the method can be expected to perform well. I also present some new technical results that provides better intuitive as well as theoretical understanding of the method. Further, I introduce a natural generalization of SSA, constructed using local (Lie-) transformation groups. The time translations (delay coordinates) used in standard SSA is a special case. The basis functions used in the decomposition then satisfy a simple type of linear ODE with time dependent coefficient, determined by the infinitesimal generator of the transformation group. Finally I will discuss future research directions, e.g., how the affine group can be used for data adaptive wavelet analysis.