SSA-MTM Toolkit

The Singular Spectrum Analysis - MultiTaper Method (SSA-MTM) Toolkit is a software program to analyze short, noisy time series, such as the one below, as well as multivariate data.

This is the so-called Southern Oscillation Index (SOI). SOI is a climatic index connected with the recurring El Niño conditions in the tropical Pacific; it is essentially the normalized monthly mean difference in sea-level pressure between Darwin, Australia and Tahiti (Rasmusson et al., 1990).

Using a convenient graphical user interface you can perform singular-spectrum analysis on input data.

SSA reconstructions of selected components and tests for the presence of trend and oscillatory components are provided. Ad hoc and Monte Carlo error bars for the SSA eigenspectra are also included. All results are displayed graphically. The next figure shows the SSA eigenspectrum for the SOI time series:

In addition, the Toolkit includes three kinds of power-spectrum estimation. These are the traditional Blackman-Tukey windowed correlogram, Multi-Taper Method (MTM), and Maximum-Entropy Method (MEM). You can apply these tools at any point in the analysis to a raw time series, or to SSA reconstructions. Outputs include power spectra and significance tests for correlogram and MTM.

The next figure shows the MTM spectrum for the same data. The black peaks are components of the spectrum tha are associated with a periodic signal, and the significance levels relative to the estimated noise background are shown.

Toolkit specifications

Toolkit version 4.0 and later utilize a convenient X-windows graphical users interface (GUI), based on X-Motif libraries. This feature makes the Toolkit more flexible in it's use and much easier to install than previous versions, insofar as X-Motif is standard on Unix computer systems. Prebuilt binary executables of the latest toolkit version are available as well in the download section.

Dynamical memory management makes the toolkit flexible for the analysis of long time series. Results and data are managed using matrices and vectors with the names supplied by the user in GUI.

The linear algebra routines in the Toolkit have been taken from the the LAPACK package.

The GUI output can be exported as postscript files. Starting with version 4.2, the toolkit supports visualization using public-domain Grace , its predessor ACE/gr, and commercial IDL plotting software (versions 5.0 and later).

Data in ASCII format can be imported into the toolkit, and can have either a single column for a single time series, or multiple columns for multiple time series.