Generalized Singular Spectrum Time Series Analysis

2002/05/31 by Martin Nilsson, Nilsson, Martin
Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Data Analysis #FOS: Physical sciences #Statistical and numerical algorithms #Statistics and Probability (physics.data-an) #physics.comp-ph #physics.data-an

paper · pdf · doi:10.48550/arxiv.physics/0205094

6 pages

arxiv created 2002/05/31 · openalex publication_date 2002/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a study of continuous time Singular Spectrum Analysis (SSA). We show that the principal eigenfunctions are solutions to a set of linear ODEs with constant coefficients. We also introduce a natural generalization of SSA, constructed using local (Lie-) transformation groups. The time translations used in standard SSA is a special case. The eigenfunctions then 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.

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