1. INTRODUCTION

The Singular Spectrum Analysis - Multitaper Method (SSA-MTM) Toolkit consists of a set of programs that perform detailed spectral analyses and decompositions on input time series (univariate or multivariate). The toolkit contains procedures for:

(a) estimating the spectrum of a time series,

(b) decomposing the time series into trends, oscillatory components, and noise, and

(c) reconstructing the contributions of selected components of the time series.

For univariate time series four methods of spectral-analysis (task a) are provided: Blackman-Tukey correlogram estimation (BT), the Maximum-Entropy Method (MEM), the Multi-Taper Method (MTM), and Singular-spectrum Analysis (SSA). SSA and MTM can then be used for separation of trends, near-periodic and other significant components, and noise (tasks b and c). Both SSA and MTM incorporate sophisticated significance tests against a variety of noise null-hypotheses, including the methods of Allen and Smith (1996) for SSA, and Mann and Lees (1996) for MTM. For multivarate time series Multi-Channel SSA method is provided.
The basic philosophy of the Toolkit is that only the simultaneous and flexible application of more than one spectral estimation method can provide truely reliable information on a given time series, when the signal-to-noise ratio is low.
This document briefly describes some of the theory behind the various methods, and demonstrates how to use the Toolkit. More details about each method can be found in the following references. Those indicated with an asterix are the central works on which the Toolikit is based:

SSA: Vautard et al. (1992)*, Allen and Smith (1996)* PDF file and test dataset, Vautard and Ghil (1989).

MTM: Mann and Lees (1996)* PDF file, Thomson (1982; 1990a-b), Percival and Walden (1993), and Yiou et al. (1991).

Blackman-Tukey correlogram estimation: Kay (1988).

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.

Section 2 gives a brief introduction to the theory behind each tool. Section 3 demonstrates the Toolkit functions. Sections 4 outlines the specifications of the Toolkit and acknowledges the many software contributions that made it possible.

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.