Elsner J., Tsonis A. Singular Spectrum Analysis: A New Tool in Time Series Analysis

Springer Science+Business Media, LLC, 1996. — XIV, 164 p.The term singular spectrum comes from the spectral (eigenvalue) decomposition of a matrix A into its set (spectrum) of eigenvalues. These eigenvalues, A, are the numbers that make the matrix A -AI singular. The term singular spectrum analysis· is unfortunate since the traditional eigenvalue decomposition involving multivariate data is also an analysis of the singular spectrum. More properly, singular spectrum analysis (SSA) should be called the analysis of time series using the singular spectrum. Spectral decomposition of matrices is fundamental to much theory of linear algebra and it has many applications to problems in the natural and related sciences. Its widespread use as a tool for time­series analysis is fairly recent, however, emerging to a large extent from applications of dynamical systems theory (sometimes called chaos theory). SSA was introduced into chaos theory by Fraedrich (1986) and Broomhead and King (l986a). Like other techniques based on spectral decomposition, SSA is attractive in that it holds a promise for a reduction in dimensionality. This reduction in dimensionality is often accompanied by a simpler explanation of the underlying physics. Singular spectrum analysis is sometimes called singular systems analysis or singular spectrum approach.Mathematical Notes
Review of Linear Algebra
Eigenvalues and Eigenvectors
Multivariate Statistics
Foundations of SSA
Details
Noise
Signal Detection
Filtering
Prediction
Phase Space Reconstruction