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

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.