USER'S GUIDE
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The Singular-Spectrum Analysis (SSA) Toolkit is a program (actually a set of programs) that performs detailed spectral analyses and decompositions on an input time series. The toolkit contains procedures for:
(a) decomposing time series into trends, quasiperiodic and periodic oscillations, other significant components, and noise,
(b) reconstructing the contributions of selected components of the time series, and
(c) estimating spectral properties of the time series or any of its components by modern spectral methods.
SSA is the method provided for separation of trends, periodic and other
significant components, and noise in the time series provided (tasks a-b
above), and three methods of spectral-analysis (task c) are provided: Blackman-Tukey
correlogram estimation, Multi-Taper Method (MTM), and Maximum-Entropy Method
(MEM). The basic philosophy of the Toolkit is that only the simultaneous
and flexible application of more than one spectral estimation method can
provide exhaustive and reliable information on a given time series. The
four methods tested and incorporated in the current version seem to complement
each other well, but do not exclude the use of additional methods in future
versions.
This document briefly describes some of the theory behind the singular-spectrum
decomposition and the spectral-analysis methods, and demonstrates how to
use the Toolkit. More details about the various procedures can be found
in:
SSA: Vautard and Ghil (1989) and Vautard et al. (1992).
Monte-Carlo SSA: Allen and Smith (1996)( compressed postscript file).
Blackman-Tukey correlogram estimation: Kay (1988).
MTM: Thomson (1982; 1990a-b), Mann and Lees (1996) ( compressed postscript file), Percival and Walden (1993), and Yio u et al. (1991).
MEM: Childers (1978), Press et al. (1989), and Penland et al. (1991).
Press et al. (1989, chapters 11 and 12) also provide excellent overviews of spectral methods and eigensystems analysis, while Manly (1986) provides a useful introduction to principal-components analysis. The description of theoretical aspects of the various procedures that follows draws heavily from these sources. However, the description is by no means an exhaustive or even complete introduction; for that, the user must become familiar with the original literature.
Section 2 describes some of the theory and theoretical considerations behind the tools provided by the Toolkit. Section 3 demonstrates many of the Toolkit functions. Sections 4 outlines the specifications of the Toolkit and acknowledges the many software contributions that made it possible. Finally, section 5 summarizes the current state of the Toolkit.
The Toolkit was developed at, and is distributed by, the University
of California, Los Angeles, with contributions from the U.S. Geological
Survey in San Diego, California, and the Commissariat à l'Énergie
Atomique in Gif-sur-Yvette, France.