500+ citations (Web of Science) for founding paper of SSA-MTM Toolkit :
Vautard, R., Yiou, P., and M. Ghil, 1992: Singular-spectrum analysis: A toolkit for short, noisy chaotic signals, Physica D, 58, 95-126.
Bibliographic references to SSA and MTM
What it is / What it does:
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 convinient 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 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 MTM spectrum for the same data. The black peaks are components of the spectrum associated with a periodic signal, and the significance levels relative to the estimated noise background are shown.
- August 24, 2015: Updated command-line Toolkit: Gap-filling added
- September 17, 2013: Minor bugs fixed.
- January 28, 2013: Major upgrade of multivariate analysis: Varimax Rotation for M-SSA . Available on Linux and Mac OS builds.
Also, beta-version (with limited features, currently mostly M-SSA) of command-line Toolkit utilities are available for Linux and Mac OS; choose "CMD for Linux" or "CMD for Mac", respectively, in download options.
- January 4, 2013: Updated 64-bit Linux and 64-bit Mac OS.
- February 4, 2008: New 64-bit bnaries for Linux and Mac OS 10.5 (Intel); 32-bit binaries for Linux and Mac OS X (Intel) recompiled with Intel compiler .
- April 12, 2007: Toolkit 4.4 (includes SSA gap-filling)!
- May 16, 2006: Universal Binary of Toolkit 4.3 for Mac OS X!
- November 11, 2005: Toolkit 4.3
- Bug, leading to crashes in MTM Reconstruction, has been fixed.
- Bug, leading to getting zero vector for MTM Reconstruction of very low-frequencies, has been fixed.
- September 26, 2003: Toolkit 4.2 (includes MSSA)!
- September 4, 2002: Toolkit ported to Mac OS 10.2 (Jaguar)!
- May 13, 2002: Minor bug is fixed in MTM when using non-deafult time step.
- March 22, 2002: Bug fixed in computing MTM with varying frequency limits.
- January 28, 2002: Mac OS X version updated for XFree86 4.2 release!
- January 23, 2002: Mac OS X version updated!(Much faster computations, check it out)
- April 11, 2001: Version 4.1 ported to Mac OS X!
- January 9, 2001: Version 4.1 ported to HP-UX!
- September 28, 2000: Version 4.1
- Graphics support for IDL (version 5.0 and later) and Grace plotting tools is added. See this guide section for more info.
- Computation speed for Monte-Carlo SSA has been optimized by fixing resolution at 0.001/dt (in the Nyquist interval from 0 to 0.5/dt) for finding dominant frequencies for EOFs.
- June 19, 2000: Version 4.0 update! MTM Confidence levels for the "white noise" null-hypothesis are plotted correctly now.
- April 5, 2000: Toolkit 4.0!
- Toolkit 4.0 is provided with a new graphical user interface (GUI) which is no longer based on TCl/Tk. 4.0 GUI is based on Motif, which is the industry standard on Unix computer systems. New GUI makes a Tollkit more flexible and easy to use.
- Dynamical memory management is implemented to remove the restrictions on the time series length, existing in the old versions of the Toolkit. The results and data are managed using matrices and vectors with the names supplied by the user in GUI.
- Linear algebra routines are now based on a latest release of LAPACK package (Version 3.0, June 1999). A considerable speed-up in Toolkit performance has been achieved.
- New plotting routines are available which allow cross-examination of the Toolkit results.
- Several minor bugs have been fixed including normalization for MTM Spectrum and choice of parameters for BT Correlogram.
Prebuilt binary executables for the Toolkit are available for download. The Toolkit has been ported and actively maintained for Linux and Mac OS X (under X11, runs natively on both PowerPC and Intel based Mac systems).
Also, legacy builds for SUN,
DEC and SGI are available
(not all latest features may be included).
Who we are:
The SSA-MTM Toolkit is a product of the SSA-MTM Group (so far: Myles Allen, Mike Dettinger, Kayo Ide, Dmitri Kondrashov, Michael Ghil, Mike Mann, Andrew W. Robertson, Amira Saunders, Ferenc Varadi, Yudong Tian, and Pascal Yiou) at UCLA (mostly). Andreas Groth helped to include VARIMAX rotation in M-SSA. Command-line version of the Toolkit is developed by Bruno Deremble and Dmitri Kondrashov.
You can direct comments on installation and performance, as well as suggestions for future versions, to firstname.lastname@example.org.
- For the application of the Toolkit in the life and biomedical sciences, please see:
A. Brawanski, R. Faltermeier, R. D. Rothoerl, C. Woertgen, 2002:
Comparison of near-infrared spectroscopy and tissue PO2 time series in
patients after severe head injury and aneurysmal subarachnoid hemorrhage.
J. Cerebr. Blood F. Met., 22 (5): 605--611.
Colebrook, J.M., 1978:
Continuous plankton records - zooplankton and environment,
northeast Atlantic and North Sea, 1948-1975,
Oceanol. Acta ,1, 9-23.
M. Grigorov, 2006: Global dynamics of biological systems from
time-resolved omics experiments, Bioinformatics, 22 (12), 1424--1430.
Mineva A, Popivanov D, 1996: Method of singletrial readiness potential
identification, based on singular spectrum analysis.
J. Neurosci. Methods, 68, 91-99.
Rodo X, Pascual M, Fuchs G, Faruque ASG, 2002:
ENSO and cholera: A nonstationary link related to climate change?
Proc. Nat. Acad. Sci. USA, 99 (20), 12901-12906.
1. ONR-N00014-12-1-0911, FY2012 Multi-University Research Initiative (MURI) Topic #16: Extended-Range Environmental Prediction Using Low-Dimensional Dynamic Modes, Office of Naval Research, 2012--2015.
2. NSF 1049253, Collaborative Research, Type 1, L02170206: Climate Sensitivity, Stochastic Models and GCM-EaSM Optimization, U.S. National Science Foundation (DMS + MPS Divisions), 2011--2014.
3. DOE DE-SC0006694, Decadal Prediction and Stochastic Simulation of Hydroclimate over Monsoonal Asia , U.S. Department of Energy, 2011--2014.
Copyright © SSA-MTM group, (mostly) UCLA.