Singular Spectrum Analysis for Time-Series Decomposition and Forecasting
Summary
The document introduces one-dimensional singular spectrum analysis (SSA) as a way to decompose a time series into components such as trend, periodic movement, and noise, then reconstruct selected components and forecast them. Basic SSA embeds the series in a sliding-window trajectory matrix, applies singular value decomposition, groups rank-one components, and uses diagonal averaging to recover component series. The article relates the rank of idealized exponential, sinusoidal, and polynomial sequences to their structure, and describes grouping through singular values and inspection of singular vectors.
Forecasting uses a linear recurrence relation derived from the selected singular vectors. A Toeplitz variant based on an autocovariance matrix is also described as more suitable for stationary series, while basic SSA is presented as preferable for nonstationary market series. The practical illustrations use synthetic series and MQL5 implementation, but the excerpt gives no general out-of-sample performance evidence. The author cautions that SSA cannot reliably distinguish deterministic trends from stochastic ones such as a Gaussian random walk; results also depend on window length and component grouping.
Key ideas
- SSA embeds observations in a Hankel trajectory matrix before applying singular value decomposition.
- Singular values and vectors help group components interpreted as trend, periodic structure, or noise.
- Diagonal averaging reconstructs time series from selected groups of elementary matrices.
- Forecasts extend reconstructed components through a linear recurrence relation derived from singular vectors.
- The choice of window and grouping affects the decomposition, and stochastic and deterministic trends can be hard to distinguish.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.