Using Singular Spectrum Analysis to Decompose, Filter, and Forecast Time Series

Summary

The article explains Singular Spectrum Analysis (SSA) as a non-parametric way to separate a time series into estimated trend, periodic components, and residual noise. It describes embedding observations into a trajectory matrix using a chosen window length, then decomposing the matrix and reconstructing component series. MQL5 vector methods provide relative component contributions, cumulative contributions, component reconstructions, filtered series, and forecasts.

The examples use a synthetic series built from trend, cycles, and random noise. The contribution spectrum can indicate dominant components and a rough elbow between signal and noise; retaining selected components yields a filtered series, while forecasting uses a recurrent linear relation. These are estimates rather than exact recovery: components may differ from the original generating parts, and their sum reconstructs the observed series. Window choice affects decomposition, low-contribution components are not necessarily noise, and strong trends can obscure oscillations. The article recommends validating interpretations statistically.

Key ideas

• SSA embeds a univariate series into a Hankel-like trajectory matrix whose dimensions depend on the window length.
• Relative eigenvalue contributions help identify dominant components and a rough signal-to-noise elbow.
• Reconstructed component series are approximations, even when their sum recovers the input series.
• Filtering and forecasts depend on component selection and the recurrent patterns in the reconstructed series.
• Window selection, noise characteristics, and strong trends limit how clearly SSA separates cycles and noise.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.