Singular Spectrum Decomposition: a New Method for Time Series Decomposition

This study introduces singular spectrum decomposition (SSD), a new adaptive method for decomposing nonlinear and nonstationary time series in narrow-banded components. The method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for analysis and prediction of time series. Unlike SSA, SSD is a decomposition method in which the choice of fundamental parameters has been completely automated. This is achieved by focusing on the frequency content of the signal. In particular, this holds for the choice of the window length used to generate the trajectory matrix of the data and for the selection of its principal components for the reconstruction of a specific component series. Moreover, a new definition of the trajectory matrix with respect to the standard SSA allows the oscillatory content in the data to be enhanced and guarantees decrease of energy of the residual. Through the numerical examples and simulations, the SSD method is shown to be able to accurately retrieve different components concealed in the data, minimizing at the same time the generation of spurious components. Applications on time series from both the biological and the physical domain are also presented highlighting the capability of SSD to yield physically meaningful components