Singular Spectrum Analysis

Singular Spectrum Analysis (SSA) is a powerful technique for analyzing and forecasting time series data that does not rely on any statistical assumptions. SSA can decompose a time series into a sum of components, such as trend, oscillation and noise, and reveal the underlying structure and dynamics of the data. SSA can also be applied to multivariate time series, change-point detection and automatic identification of components. The algorithm of SSA consists of four main steps: embedding, decomposition, grouping and reconstruction. Embedding transforms the time series into a trajectory matrix using delayed coordinates. Decomposition performs the singular value decomposition (SVD) of the trajectory matrix and obtains the eigenvalues, eigenvectors and principal components. Grouping combines the principal components into different groups according to some criteria. Reconstruction reconstructs the components of the time series from the groups of principal components using the inverse of the embedding. In this chapter we review the theoretical and methodological aspects of SSA from the perspective of analyzing and forecasting the simulated and real time series data using Rssa package.