Improving reconstruction of time-series based in Singular Spectrum Analysis: A segmentation approach

Singular Spectrum Analysis (SSA) is a powerful non-parametric framework to analysis and enhancement of time-series. SSA may be capable of decomposing a time-series into its meaningful components: trends, oscillations and noise. However, if the signal under analysis is non-stationary, with its spectrum spreading and varying in time, the reliability of the reconstruction is guaranteed only when many elementary matrices are used. As a consequence, the capability to discriminate dominant structures from time-series may be impaired. To circumvent this issue, a new method, called overlap-SSA (ov-SSA), is proposed for segmentation, analysis and reconstruction of long-term and/or non-stationary signals. The raw time series is divided into smaller, consecutive and overlapping segments, and standard SSA procedures are applied to each segment with the resulting series being concatenated. This variation of SSA seeks to: improve reconstruction and component separability for non-stationary time-series; enable the analysis for large datasets, avoiding the issues of concatenation of many segments; and present some benefits of the segmentation in terms of better time-frequency characterization. These advantages are illustrated in several synthetic and experimental datasets.