This project explores how Topological Data Analysis (TDA) can enhance N-BEATS, a powerful deep learning model for time series forecasting.
Our goal is to improve market prediction accuracy by integrating geometric insights from TDA with N-BEATS’ interpretable and modular forecasting architecture.
TDA is a mathematical framework that studies the shape and structure of data rather than relying only on statistical summaries.
It captures persistent topological features—like clusters, loops, and voids—that represent the underlying geometry of the dataset.
This helps distinguish meaningful structures from noise across multiple scales.
N-BEATS is a deep neural architecture designed specifically for interpretable time series forecasting.
It models complex temporal patterns using stacks of fully connected blocks that decompose data into trend and seasonal components.
- Interpretability: Identifies which components of the data drive predictions.
- Modularity: Built from configurable blocks, allowing flexibility without changing the core architecture.
- Generalization: Performs well across diverse datasets without task-specific tuning.
To date, no existing research directly investigates using TDA for forecasting tasks.
This project aims to bridge that gap—combining geometric data analysis with modern forecasting networks to uncover deeper temporal structures in financial data.
We use the Yahoo Finance S&P 500 dataset, containing historical daily closing prices of the top 500 U.S. publicly traded companies.
We focus initially on a univariate forecasting problem:
Predicting future closing prices based on past lagged values.
We apply a sliding window technique to segment the time series into overlapping windows of fixed length.
Each window is used for two purposes:
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TDA Feature Extraction:
- Convert each window into a point cloud via time-delay embedding.
- Extract topological features (e.g., persistent homology) representing the window’s geometric structure.
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Forecasting Input (N-BEATS):
- Use the same windows as sequential inputs for model training and validation.
- Enables consistent temporal alignment between TDA features and model inputs.
This ensures seamless integration of topological structure with data-driven forecasting.
We will compare the baseline N-BEATS model against our TDA-enhanced N-BEATS.
- Mean Absolute Error (MAE)
- Root Mean Squared Error (RMSE)
- Mean Absolute Percentage Error (MAPE)
Success = Lower error and more consistent forecasts from the TDA-enhanced model compared to the baseline.
- Base Model: N-BEATS (Neural Basis Expansion Analysis for Interpretable Time Series Forecasting)
- Enhanced Model: N-BEATS + TDA features
We aim to answer the research question:
How does the TDA + N-BEATS model perform compared to the baseline N-BEATS model in forecasting accuracy (MAE, RMSE, MAPE)?
- Data Bias: The S&P 500 focuses on large U.S. companies, possibly limiting generalization to smaller or non-U.S. markets.
- Temporal Bias: Model performance may degrade during structural shifts (e.g., recessions, crises).
- Feature Bias: TDA features may emphasize geometric patterns that don’t actually correlate with future price behavior.
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de Jesus, Luiz Carlos, et al. (2025).
Enhancing Financial Time Series Forecasting through Topological Data Analysis.
Neural Computing and Applications, 37(9), 6527–6545.
https://doi.org/10.1007/s00521-024-10787-x -
Nixtla. (2019).
N-BEATS — Nixtla NeuralForecast Library.
https://nixtlaverse.nixtla.io/neuralforecast/models.nbeats.html -
Yahoo Finance. (2025).
Yahoo Finance — Business, Market Data, News.
https://finance.yahoo.com/
This project is released under the MIT License.