Stat Methods Appl (2017) 26:361–382
Multivariate posterior singular spectrum analysis
· Lasse Holmström
Accepted: 11 October 2016 / Published online: 27 October 2016
© Springer-Verlag Berlin Heidelberg 2016
Abstract A generalized, multivariate version of the Posterior Singular Spectrum
Analysis (PSSA) method is described for the identiﬁcation of credible features in
multivariate time series. We combine Bayesian posterior modeling with multivariate
SSA (MSSA) and infer the MSSA signal components with a credibility analysis of
the posterior sample. The performance of multivariate PSSA (MPSSA) is compared
to the single-variate PSSA with an artiﬁcial example and the potential of MPSSA is
demonstrated with real data using NAO and SOI climate index series.
Keywords Time series · SSA · Bayesian inference · Multivariate · Climate index
Singular spectrum analysis (SSA) is a broad methodology of time series analysis whose
applications include e.g. smoothing, noise reduction, extraction of trend and periodic-
ities, missing data imputation and forecasting. SSA is an algebraic technique without
any statistical model or stationarity assumptions. SSA is based on the singular value
decomposition of an embedded time series and is thus related to principal component
analysis. The original series, decomposed into ‘eigentriples’ of singular values and
their associated eigenvectors, is regrouped to form various component series, which
may be interpreted as a slowly-varying trend, periodic series and noise.
Ilkka Launonen: Research supported by Academy of Finland Project No. 250862 and a grant from the
Alfred Kordelin Foundation.
Lasse Holmström: Research supported by Academy of Finland Project No. 250862.
Department of Mathematical Sciences, University of Oulu, Oulu, Finland