Topological data analysis (TDA) is increasingly acknowledged within financial markets for its capacity to manage complexity and discern nuanced patterns and structures. It has been applied effectively to uncover intricate relationships and capture non-linear dependencies inherent in market data. This manuscript presents a groundbreaking study that delves into integrating features derived from TDA to improve the performance of forecasting models for univariate time series prediction. The research specifically examines whether incorporating features extracted from TDA-such as entropy, amplitude, and the number of points obtained from persistent diagrams can provide valuable supplementary information to the baseline forecasting model. Thus, the aim is to determine if these TDA-derived features can boost forecasting accuracy by offering additional insights that existing models might overlook. The model serves as the baseline forecasting model due to its robust generalization capabilities and flexibility in incorporating additional features into the model. The proposed methodology is compared against a univariate model without additional features and other strategies incorporating supplementary features such as temporal decomposition and time delay embeddings. The evaluation includes forecasting for six cryptocurrencies across four distinct time scenarios and four traditional financial instruments across two scenarios each, resulting in 32 datasets. The results obtained were promising, as the proposed method, $$\texttt {N-BEATS}_\mathrm {+TDA}$$ N - BEATS + TDA , achieved the best results in mean performance and mean ranking for the three metrics considered (MAPE, MAE, and RMSE). Significant differences were observed with the rest of the proposed methods using a significance level of $$\alpha = 0.10$$ α = 0.10 , highlighting the effectiveness of integrating TDA features to enhance forecasting models.

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.