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Enhancing financial time series forecasting through topological data analysis

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Bibliographic Details
Title: Enhancing financial time series forecasting through topological data analysis
Authors: Luiz Carlos de Jesus, Francisco Fernández-Navarro, Mariano Carbonero-Ruz
Source: RIUMA. Repositorio Institucional de la Universidad de Málaga
Universidad de Málaga
Publisher Information: Springer Science and Business Media LLC, 2025.
Publication Year: 2025
Subject Terms: Time series forecasting, Análisis de datos, Topological data analysis, Feature extraction
Description: 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.
Document Type: Article
Language: English
ISSN: 1433-3058
0941-0643
DOI: 10.1007/s00521-024-10787-x
Access URL: https://hdl.handle.net/10630/36603
Rights: CC BY
Accession Number: edsair.doi.dedup.....2dea88c4beed8a19faab4ba4335dd095
Database: OpenAIRE
Description
Abstract: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.
ISSN:14333058
09410643
DOI:10.1007/s00521-024-10787-x