Particularities and commonalities of singular spectrum analysis as a method of time series analysis and signal processing

Abstract

Singular spectrum analysis (SSA), starting from the second half of the XX century, has been a rapidly developing method of time series analysis. Since it can be called principal component analysis for time series, SSA will definitely be a standard method in time series analysis and signal processing in the future. Moreover, the problems solved by SSA are considerably wider than that for principal component analysis. In particular, the problems of frequency estimation, forecasting and missing values imputation can be solved within the framework of SSA. The idea of SSA came from different scientific communities, such as that of researchers in time series analysis (Karhunen-Loeve decomposition), signal processing (low-rank approximation and frequency estimation) and multivariate data analysis (principal component analysis). Also, depending on the area of applications, different viewpoints on the same algorithms, choice of parameters, and methodology as a whole are considered. Thus, the aim of the paper is to describe and compare different viewpoints on SSA and its modifications and extensions to give people from different scientific communities the possibility to be aware of potentially new aspects of the method.