The SSA Toolkit is provided with a convenient X-windows graphical users' interface (GUI) that was developed using the wish windowing shell, Tk X-window toolkit, and Tcl command language (Ousterhout, 1994). Together, wish, Tk, and Tcl provide a shell that allows the Toolkit components to be launched effortlessly from X-window environments. Several Tk extensions, written by Jim Davidson and Terry Figel at the Center for Remote Sensing and Environmental Optics, UC Santa Barbara, were incorporated to make the Toolkit easier to use.
Currently, the main Toolkit components are contained infiver numerical programs:
Each program is functional in a stand-alone mode, i.e., without the GUI, on any computer with a standard FORTRAN 77 compiler. These programs are structured as Unix commands and can be invoked in batch mode by shell scripts. HTML pages are provided with the Toolkit distribution for each of these programs to explain their usage. Much guidance for the development of these programs was obtained from earlier SSA and MEM codes written and provided by Cecile Penland of the University of Colorado, Boulder. Source code for some of the eigenanalysis routines was from the SLATEC library, a public domain package provided by the National Energy Software Center in Argonne, Illinois.
The GUI displays time series, eigenvalues (variance) spectra, and power spectra to windows. It can also--through the graphics packages used to display Toolkit graphs-- copy these to Postscript files for printing. The visualization requirements to generate and display these graphs are relatively simple, and the Toolkit has been designed so that different graphics packages can be accommodated. Currently the Toolkit supports visualization using IDL (a proprietary package by Research Systems, Inc.) or the public-domain ACE/gr and gnuplot plotting programs.
The SSA Toolkit is configured for analysis of a univariate time series, and thus expects a series {x(i),i=1,...,N} as input. Practical size constraints on Toolkit analyses arise from the width of the SSA or correlogram windows or the number of Monte Carlo realizations used to form error bars, rather than the length of the time series. Most matrices to be diagonalized in the various procedures have dimensions equal to these window lengths, that determine the computational times and memory requirements. As a practical matter, window widths should be less than about 300-500, but such limits depend on the size and speed of the computational device--workstation or mainframe--used. An exception to this "rule" is the Burg estimate of autocorrelation structures for SSA and AR coefficients for MEM; for long series (order of 5,000 samples), this algorithm can be time consuming also.
Time series can be input in the following formats:
As indicated, Toolkit outputs take the form of postscript graphics, ASCII tables and logs, and ASCII vectors, series and power spectra.
Questions, suggestions, and bug reports should be sent to ssahelp@atmos.ucla.edu .
The Toolkit is an evolving package and we encourage feedback on its form and future. We will make every effort to help you get the most from the Toolkit.
The Singular-Spectrum Analysis (SSA) Toolkit was designed to make certain modern forms of time-series spectrum analysis more accessible to Earth scientists. These spectral tools--especially SSA--have not been available in previous statistical packages. We hope that enhanced accessibility will lead to frequent use in varied applications. In a matter of minutes, [i] any univariate time series can be decomposed to isolate periodic and trend components, [ii] its power spectrum evaluated by modern methods including Multi-Taper Method and Maximum-Entropy Method, both before and after filtering with the SSA procedures, and [iii] selected trends, oscillations, and other structured components of the signal can be put out (or further analyzed) for other uses. The analytical power and user-friendliness of the Toolkit are a promising combination that should make analysis of large geophysical datasets much more tractable.
The current Toolkit presents one "complete basis" for spectral analysis of univariate time series in the sense that all the tools for a complete analysis using SSA are provided; however, it has been designed specifically with expansion in mind. There are literally dozens of other modern spectral-analysis methods available, and the potential for development of additional methods is far from exhausted. Further elaboration of the confidence tests for SSA (including that of Allen and Smith [1994]) and Multi-Taper Method is also under development and may appear in future versions of the Toolkit. Similarly, a number of alternatives to univariate SSA are available. SSA has recently been extended to a multi-channel form that has allowed powerful analyses of time-varying climatic fields (e.g., Kimoto et al., 1991; Keppenne and Ghil, 1993). Used together with spatial EOF analyses to reduce spatial dimensionality, multi-channel SSA (M-SSA) can provide remarkable efficiency in analysis of massive climatic datasets. Consequently, addition of M-SSA capabilities to the SSA Toolkit is a near-term priority. Room also exists in the Toolkit for addition of such procedures as principal-oscillation-pattern analyses (e.g., Penland and Magorian, 1993) and canonical-correlation analyses (e.g., Barnett et al. 1988). Although the Toolkit is not intended to be a comprehensive time-series analysis package, additions and contributions are welcomed and will be incorporated when possible.
The development and application of SSA to geophysical time series was carried out by the present authors in collaboration with N. Jiang, C.L. Keppenne, K.-C. Mo, J.D. Neelin, M.C. Penland, G. Plaut, A.W. Robertson, Y. Sezginer, S. Speich, and R. Vautard. Comments by these collaborators and numerous other colleagues on test versions of the Toolkit are gratefully acknowledged. The Toolkit was developed mostly on equipment and with support provided by Digital Equipment Corporation to the University of California, Los Angeles, Department of Atmospheric Sciences, as part of the Sequoia 2000 project. Research for the development of the methods and their applications to climatic time series was supported by NSF Grant ATM93-13217, NOAA Grant NA36G90245, and an NSF Special Creativity Award to M. Ghil. Use of trade names in this article is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey.