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

• Published in: Journal of Climate
• Main Authors: Groth, Andreas, Ghil, Michael
• Other Authors: Institute of Geophysics and Planetary Physics Los Angeles (IGPP), University of California Los Angeles (UCLA), University of California (UC)-University of California (UC), Department of Atmospheric and Oceanic Sciences Los Angeles (AOS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2015
• Subjects: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; [STAT.AP]Statistics [stat]/Applications [stat.AP]; [STAT.ME]Statistics [stat]/Methodology [stat.ME]; [SDU.OCEAN]Sciences of the Universe [physics]/Ocean; Atmosphere; North Atlantic; North Atlantic oscillation
• Online Access: https://hal.archives-ouvertes.fr/hal-01701132; https://hal.archives-ouvertes.fr/hal-01701132/document; https://hal.archives-ouvertes.fr/hal-01701132/file/Procrustes_JCLI-reprint.pdf; https://doi.org/10.1175/JCLI-D-15-0100.1

International audience Singular spectrum analysis (SSA) along with its multivariate extension (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 reexamined, 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.