A New Approach to SSA Trajectory Matrix Construction Based on Subseries Partitioning
Rahim Mahmoudvand, Paulo Canas Rodrigues · Fluctuation and Noise Letters · 2025
Singular Spectrum Analysis (SSA) is a versatile tool for analyzing both univariate and multivariate time series. In traditional univariate SSA, the data are embedded into a Hankel matrix to extract meaningful components through matrix decomposition, multivariate SSA, generalize this by stacking Hankel matrices from multiple related time series. This paper introduces a new form of trajectory matrix construction for univariate SSA, inspired by the structure of MSSA. The key idea is to transform a univariate time series into a multivariate form through a thinning process, dividing the series into subsets of data points. This transformation leverages the dependence between different points in the time series while enabling the application of multivariate methods. Such an approach is particularly advantageous for long time series with periodic patterns, such as hourly data, where thinning can effectively capture the underlying structure. We provide theoretical results that demonstrate the potential superiority of the proposed method in terms of model fitting. These findings are supported by extensive simulations and applications to real-world data, including the UKgas, USAccDeaths time series, which confirm the improved performance of the method in both fitting and forecasting tasks.