Multichannel Singular Spectrum Analysis - Beginners guide
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.
Cite As
Andreas Groth (2024). Multichannel Singular Spectrum Analysis - Beginners guide (https://www.mathworks.com/matlabcentral/fileexchange/58968-multichannel-singular-spectrum-analysis-beginners-guide), MATLAB Central File Exchange. Retrieved .
MATLAB Release Compatibility
Platform Compatibility
Windows macOS LinuxCategories
Tags
Acknowledgements
Inspired by: Singular Spectrum Analysis - Beginners guide
Inspired: Multichannel Singular Spectrum Analysis - varimax tutorial
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Discover Live Editor
Create scripts with code, output, and formatted text in a single executable document.
html/
Version | Published | Release Notes | |
---|---|---|---|
3.0.0.0 |
Description updated
|