Methodology
In practice, SSA is a nonparametric spectral estimation method based on embedding a time series in a vector space of dimension . SSA proceeds by diagonalizing the lag-covariance matrix of to obtain spectral information on the time series, assumed to be stationary in the weak sense. The matrix can be estimated directly from the data as a Toeplitz matrix with constant diagonals (Vautard and Ghil, 1989), i.e., its entries depend only on the lag :
An alternative way to compute, is by using the ``trajectory matrix" that is formed by lag-shifted copies of, which are long; then
The eigenvectors of the lag-covariance matrix are called temporal empirical orthogonal functions (EOFs). The eigenvalues of account for the partial variance in the direction and the sum of the eigenvalues, i.e., the trace of, gives the total variance of the original time series . The name of the method derives from the singular values of
Read more about this topic: Singular Spectrum Analysis
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“One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views, fairy tales, instead of the customary pair theory/observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is rather to convince the reader that all methodologies, even the most obvious ones, have their limits.”
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