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Abstract
The extraction of essential features from real-valued time series is fundamental for exploration, modeling, and forecasting. Singular Spectrum Analysis (SSA) transforms a time series into a Hankel trajectory matrix, which is decomposed by Singular Value Decomposition (SVD) into rank-one matrices that can be grouped to represent components such as trend, oscillations, and noise.
The structure of a time series is closely related to the eigenvectors of its trajectory matrix, making their graphical representation a useful tool for visual interpretation. Using the SSA-based trajectory matrix and its decomposition via Partial Least Squares, we adopt a biplot-based visualization approach. In particular, we explore the HJ-biplot, which provides a high-quality simultaneous representation of rows and columns and discuss its interpretation for Hankel trajectory matrices.
We also address the detection of structural changes in time series. Unlike traditional SSA-based methods that compare decompositions of different trajectory matrices, we propose a new approach that compares two NIPALS-based decompositions of the same trajectory matrix.
An illustrative example is provided to show how those trajectory matrix decompositions can be used to visualize key time series features and identify potential structural changes.
Short Bio
Adelaide Freitas is currently an Associate Professor in the Department of Mathematics at University of Aveiro (Portugal) and the scientific coordinator of the Probability and Statistics Group at the Centre for Research and Development in Mathematics and Applications (CIDMA). She has several publications in Statistics, covering Multivariate Statistics (dimensionality reduction), Extreme Value Theory, and the Teaching of Probability and Statistics, and has presented at numerous scientific conferences. She has contributed to the organization of both national and international conferences, as well as multiple workshops in the field of Statistics. She has participated in teaching mobility programs (Erasmus). Identifiers: ORCID: 0000-0002-4685-1615 | SCOPUS Author ID: 12793825900 | CIÊNCIAVITAE ID: E318-08D6-3E4F.
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