Matlab tutorials

The SSA and M-SSA tutorials demonstrate step by step the single- and multichannel version of a singular spectrum analysis (SSA). The steps are similar in both versions and include

  1. the creation of the trajectory matrix,
  2. calculation of the covariance matrix,
  3. eigendecomposition of the covariance matrix,
  4. the resulting eigenvalues, eigenvectors,
  5. the calculation of the principal components,
  6. the reconstruction of the signal component.

The tutorials also explain the difference between the Toeplitz approach of Vautard and Ghil (1989) and the trajectory approach of Broomhead and King (1986). Note that only the latter approach ensures a positive semi-definite covariance matrix with non-negative eigenvalues; cf. also Ghil et al. (2002) and Groth and Ghil (2015) for a review.

The M-SSA varimax tutorial demonstrates the application of the varimax algorithm to the eigenvectors of a multichannel singular spectrum analysis (M-SSA). The special structure of the M-SSA eigenvectors requires a modification of the original varimax  algorithm. For more mathematical details see Groth and Ghil (2011).