Monte Carlo Singular Spectrum Analysis (SSA) Revisited: Detecting Oscillator Clusters in Multivariate Datasets

Abstract

Multichannel singular spectrum analysis (M-SSA) provides an efficient way to identify weak oscillatory behavior in high-dimensional data. To prevent the misinterpretation of stochastic fluctuations in short time series as oscillations, Monte Carlo (MC)-type hypothesis tests provide objective criteria for the statistical significance of the oscillatory behavior. Procrustes target rotation is introduced here as a key method for refining previously available MC tests. The proposed modification helps reduce the risk of type-I errors, and it is shown to improve the test's discriminating power. The reliability of the proposed methodology is examined in an idealized setting for a cluster of harmonic oscillators immersed in red noise. Furthermore, the common method of data compression into a few leading principal components, prior to M-SSA, is re-examined and its possibly negative effects are discussed. Finally, the generalized Procrustes test is applied to the analysis of interannual variability in the North Atlantic's sea surface temperature and sea level pressure fields. The results of this analysis provide further evidence for shared mechanisms of variability between the Gulf Stream and the North Atlantic Oscillation in the interannual frequency band.

Interannual Variability in the North Atlantic Ocean’s Temperature Field and Its Association with the Wind Stress Forcing

“…In this context, Groth and Ghil (2015) found the Procrustes algorithm helpful in comparing the data eigendecomposition with that of the surrogate data generated by the red-noise null hypothesis, and showed that application of this algorithm substantially improves the explanatory power of the test. These authors further provided a rigorous mathematical extension of a composite null hypothesis test for M-SSA: for instance, a strong trend component can be excluded from the raw data when estimating the parameter of the null hypothesis.…”

“…This compression of the dataset into a few leading PCs is meant to reduce the computational costs of a subsequent M-SSA analysis (e.g., Dettinger et al 1995;Allen and Robertson 1996;Robertson 1996); see also Moron et al (1998) and Table 1 therein. Groth and Ghil (2015), though, have demonstrated possible negative effects of this variance compression on the detection rate of weak signals when the number of retained PCs becomes too small. In appendix B, we demonstrate that this practice can further affect negatively the judicious reconstruction of the spatio-temporal patterns of such weak signals, and recommend retaining a maximum number of PCs.…”

“…2, with the spectrum of eigenvalues and the corresponding significance levels in panel (a). The latter levels have been derived from a composite null hypothesis of the leading ST-EOF 1 plus AR(1) noise; see Groth and Ghil (2015) for more methodological details.…”

“…To this end, we have devised a protocol related to the classical M-SSA null-hypothesis test (Allen and Smith 1996;Groth and Ghil 2015), to test the hypothesis of interannual variability in the ocean being a response to similar variability in the atmospheric forcing. The present method complements, therefore, the common approach of comparing multiple realizations of an ocean general circulation model, driven with different atmospheric forcings (e.g., Grégorio et al 2015;Sérazin et al 2015).…”

Pathogens trigger top-down climate forcing on ecosystem dynamics

“…However, to avoid any misinterpretation of random fluctuations as oscillations, we performed a Monte Carlo statistical test and compared the variance captured by each pair of ST-EOFs with that in a large ensemble of random-walk noise surrogates (Allen and Robertson 1996;Allen and Smith 1996;Groth and Ghil 2015). In this analysis, we considered 21 ST-EOF pairs.…”