Statistics and Its Interface

Volume 10 (2017)

Number 1

Semi-nonparametric singular spectrum analysis with projection

Pages: 47 – 57

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n1.a5

Authors

Nina Golyandina (Department of Statistical Modeling, St. Petersburg State University, St. Petersburg, Russia)

Alex Shlemov (Department of Statistical Modeling, St. Petersburg State University, St. Petersburg, Russia)

Abstract

Singular spectrum analysis (SSA) is a technique of time series analysis. The Basic SSA method is nonparametric and constructs an adaptive decomposition based on the singular value decomposition (SVD). We propose a modification of Basic SSA which we call SSA with projection. This version of SSA is able to take into consideration a structure given in advance. SSA with projection includes preliminary projection of rows and columns of the series’ trajectory matrix to given subspaces. One application of SSA with projection is the extraction of polynomial trends. It is demonstrated that SSA with projection can extract polynomial trends much better than Basic SSA, especially in the case of linear trends. Numerical examples, including comparison with the leastsquares polynomial regression, are presented.

Keywords

singular spectrum analysis, time series, time series decomposition, separability, regression

2010 Mathematics Subject Classification

Primary 62G05, 94A12. Secondary 37M10, 60G35.

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