Finding stationary subspaces in multivariate time series

Identifying temporally invariant components in complex multivariate time series is key to understanding the underlying dynamical system and predict its future behavior. In this Letter, we propose a novel technique, stationary subspace analysis (SSA), that decomposes a multivariate time series into i...

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Bibliographic Details
Published in:Physical review letters 2009-11, Vol.103 (21), p.214101-214101, Article 214101
Main Authors: von Bünau, Paul, Meinecke, Frank C, Király, Franz C, Müller, Klaus-Robert
Format: Article
Language:English
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Summary:Identifying temporally invariant components in complex multivariate time series is key to understanding the underlying dynamical system and predict its future behavior. In this Letter, we propose a novel technique, stationary subspace analysis (SSA), that decomposes a multivariate time series into its stationary and nonstationary part. The method is based on two assumptions: (a) the observed signals are linear superpositions of stationary and nonstationary sources; and (b) the nonstationarity is measurable in the first two moments. We characterize theoretical and practical properties of SSA and study it in simulations and cortical signals measured by electroencephalography. Here, SSA succeeds in finding stationary components that lead to a significantly improved prediction accuracy and meaningful topographic maps which contribute to a better understanding of the underlying nonstationary brain processes.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.103.214101