Generalized Singular Spectrum Time Series Analysis

Organized by the Complex Systems Modeling Team of the Computer Research and Applications Group.

Martin Nilsson, Los Alamos National Laboratory, Hydrology, Geochemistry and Geology Group(EES-6).

August 14th, CNLS Conference Room, 2:00-3:30pm

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.

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Last Modified: August 12, 2002