SSA-Aid: Intelligent Decomposition into Trend, Periodicities, and Noise Using Singular Spectrum Analysis

Abstract

Automatic decomposition of a time series into trend, periodicities, and noise remains open in singular spectrum analysis (SSA): trend extraction is reliably automated, but automatic identification of periodic components is still challenging, especially for weakly separated or non-dominant components. We propose SSA-Aid, a modular framework inferring the number and structure of periodic components from the data. It includes separability improvement and two complementary periodicity-identification strategies with an empirical stopping rule against over-extraction. Its most general variant, SSA-AidMC, extracts dominant and non-dominant components using Monte Carlo SSA and refines them jointly. In the tested configurations, both strategies perform well on four synthetic examples, while SSA-AidMC provides consistent gains for non-dominant components, including those with modulated amplitudes. In forecasting, no single method dominates; standalone SSA variants are more accurate in some signal structures, conventional baselines or hybrid variants (SSA decomposition with an external trend forecaster) in others. The framework uses generic tuning parameters with recommended defaults, and its main computational cost comes from repeated MC-SSA assessments, each requiring a fixed number of surrogate series. This cost is the price of its central advantage: no seasonal periods or functional forms must be specified within the general SSA signal model.

The authors' abstract, as published at the source. Algorithms, 2026 · DOI ↗