The Singular Spectrum Analysis - Multitaper Method (SSA-MTM) Toolkit provides a set of statistical tools for detailed spectral analyses and decompositions of input time series (univariate or multivariate). The toolkit contains procedures to
- estimate the spectrum of a time series
- decompose the time series into trend, oscillatory components, and noise
- reconstruct parts of the time series that belong to specific components.
For univariate time series, four methods of spectral-analysis 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 furthermore separate the time series into a trend, oscillatory components, and noise. 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 are provided. For multivarate time series a multichannel version of SSA (M-SSA) is implemented, with an optional varimax rotation.
This documentation briefly describes some of the theoretical ideas behind the four methods, and gives a demonstration of the graphical user interface. More mathematical details about the individual method can be found in the following references. Those indicated with an asterix (*) are central for the toolkit.
MTM: Mann and Lees (1996)*, 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 eigenanalysis, while Manly (1986) provides a useful introduction to principal component analysis.
|For a recent review of SSA, M-SSA, the varimax algorithm as well as the statistical significance test see Groth and Ghil (2015).|