Topological Data Analysis for Financial Time Series Forecasting: A Persistent Homology Approach

We present a methodological framework integrating topological data analysis (TDA) with deep learning for financial forecasting. TDA extracts geometric features from market data through persistent homology, capturing multi-scale patterns overlooked by traditional methods. We validate the approach on EUR/USD high-frequency data (2020–2023), combining topological features with CNN-LSTM networks. The TDA-enhanced model achieves 67.3% directional accuracy versus 54.2% baseline (24% improvement), Sharpe ratio of 2.14 versus 0.87 (146% increase), and maximum drawdown of -5.9% versus -12.3% (52% reduction). Topological features exhibit strong correlation with volatility (ρ = 0.73) and provide early signals for market events. Despite promising results, computational costs, parameter sensitivity, and limited validation scope require further research before practical deployment.