Multichannel Singular Spectrum Analysis - Beginners guide

Step-by-step tutorial of multichannel singular spectrum analysis (M-SSA)

This Matlab tutorial demonstrates step by step the multichannel version of a singular spectrum analysis (SSA), a nonparametric spectral estimation method for multivariate time series. The guide explains the following steps of an SSA analysis
- creation of the trajectory matrix
- calculation of the covariance matrix
- eigendecomposition of the covariance matrix
- resulting eigenvalues, eigenvectors
- calculation of the principal components
- reconstruction of the time series.
The tutorial also explains the difference between the Toeplitz approach of Plaut and Vautard (1994) 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. For a review of SSA see Ghil et al. (2002) and Groth and Ghil (2015).
References
Broomhead, D. S., and G. P. King, 1986: On the qualitative analysis of experimental dynamical systems, Nonlinear Phenomena and Chaos , Sarkar, S. (Ed.), Adam Hilger, 113-144.

Ghil, M., M. R. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M. E. Mann, A. W. Robertson, A. Saunders, Y. Tian, F. Varadi, and P. Yiou, 2002: Advanced spectral methods for climatic time series, Reviews of Geophysics, 40, 1-41

Groth, A., and M. Ghil, 2015: Monte Carlo Singular Spectrum Analysis (SSA) revisited: Detecting oscillator clusters in multivariate datasets, Journal of Climate, 28, 7873-7893.

Plaut, G., and R. Vautard, 1994: Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere, Journal of the Atmospheric Sciences, 51, 210-236.