Singular spectrum time–series analysis and continuous transformation groups

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Nilsson Martin 2004Singular spectrum time–series analysis and continuous transformation groupsProc. R. Soc. Lond. A.460929–938http://doi.org/10.1098/rspa.2003.1197SectionRestricted accessResearch articleSingular spectrum time–series analysis and continuous transformation groups Martin Nilsson Martin Nilsson Nordic Institute of Theoretical Physics (NORDITA), Blegdamsvej 17, 2100 Copenhagen, Denmark () Google Scholar Find this author on PubMed Search for more papers by this author Martin Nilsson Martin Nilsson Nordic Institute of Theoretical Physics (NORDITA), Blegdamsvej 17, 2100 Copenhagen, Denmark () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 March 2004https://doi.org/10.1098/rspa.2003.1197AbstractThis paper is a study of continuous–time singular spectrum analysis (SSA). We show that the principal eigenfunctions are solutions to a set of linear ordinary differential equations (ODEs) with constant coefficients. We also introduce a natural generalization of SSA, based on using local (Lie–) transformation groups to construct the trajectory function. The time translations (delay coordinates) used in standard SSA is a special case. A general relation between the transformation group used in the construction of the trajectory matrix and the principal eigenfunctions is demonstrated. The eigenfunctions satisfy a simple type of linear ODE with time–dependent coefficient, determined by the infinitesimal generator of the transformation group. Finally, more general one–parameter mappings are considered. Previous Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Golyandina N and Zhigljavsky A (2020) Introduction Singular Spectrum Analysis for Time Series, 10.1007/978-3-662-62436-4_1, (1-20), . This Issue08 March 2004Volume 460Issue 2043 Article InformationDOI:https://doi.org/10.1098/rspa.2003.1197Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/03/2004Published in print08/03/2004 License: Citations and impact KeywordsTime–Series AnalysisSpectral MethodsPrincipal Component AnalysisSpectral AnalysisSingular Spectrum AnalysisLie Groups