Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package

Nina Golyandina (1) , Anton Korobeynikov (1) , Alex Shlemov (1) , Konstantin Usevich (2)

1 Mathematics and Mechanics Faculty [St Petersbourg]
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

Implementation of multivariate and 2D extensions of Singular Spectrum Analysis (SSA) by means of the R-package Rssa is considered. The extensions include MSSA for simultaneous analysis and forecasting of several time series and 2D-SSA for analysis of digital images. A new extension of 2D-SSA analysis called Shaped 2D-SSA is introduced for analysis of images of arbitrary shape, not necessary rectangular. It is shown that implementation of Shaped 2D-SSA can serve as a base for implementation of MSSA and other generalizations. Efficient implementation of operations with Hankel and Hankel-block-Hankel matrices through FFT is suggested. Examples with code fragments in R, which explain the methodology and demonstrate the proper use of Rssa, are presented.

Mots clés: singular spectrum analysis; time series; image processing; analysis; forecasting; decomposition; R package

Domaines: Méthodologie [stat.ME]

Nina Golyandina, Anton Korobeynikov, Alex Shlemov, Konstantin Usevich. Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package. Journal of Statistical Software, 2014, 67 (2), pp.1-78. ⟨hal-01066695⟩