de Jesus Jr, Luiz Carlos , Fernandez-Navarro, Francisco , CARBONERO RUZ, MARIANO
No
Mathematics
Article
Científica
02/02/2026
001688013400001
2-s2.0-105030144248
A principled, model-agnostic framework for structural feature extraction in time series is presented, grounded in topological data analysis (TDA). The motivation stems from two gaps identified in the literature: First, compact and interpretable representations that summarise the global geometric organisation of trajectories across scales remain scarce. Second, a unified, task-agnostic protocol for evaluating structure preservation against established non-topological families is still missing. To address these gaps, time-delay embeddings are employed to reconstruct phase space, sliding windows are used to generate local point clouds, and Vietoris-Rips persistent homology (up to dimension two) is computed. The resulting persistence diagrams are summarised with three transparent descriptors-persistence entropy, maximum persistence amplitude, and feature counts-and concatenated across delays and window sizes to yield a multiscale representation designed to complement temporal and spectral features while remaining computationally tractable. A unified experimental design is specified in which heterogeneous, regularly sampled financial series are preprocessed on native calendars and contrasted with competitive baselines spanning lagged, calendar-driven, difference/change, STL-based, delay-embedding PCA, price-based statistical, signature (FRUITS), and network-derived (NetF) features. Structure preservation is assessed through complementary criteria that probe spectral similarity, variance-scaled reconstruction fidelity, and the conservation of distributional shape (location, scale, asymmetry, tails). The study is positioned as an evaluation of representations, rather than a forecasting benchmark, emphasising interpretability, comparability, and methodological transparency while outlining avenues for adaptive hyperparameter selection and alternative filtrations.
topological data analysis; structural preservation; time-series feature extraction; interpretable representation learning