Fractal memory and deep learning: A new paradigm for stock market prediction

Stock market forecasting remains challenging due to strong nonlinearity, volatility, and no stationarity inherent in financial time series. Accurate price prediction is therefore essential for informed decision-making in financial markets. Traditional statistical models often fail to capture these complex dynamics, motivating the use of hybrid deep learning approaches. In this study, fractal characteristics of financial time series are incorporated into deep learning models through the rolling Hurst exponent to capture long-term memory effects. Three hybrid forecasting frameworks are developed: LSTM-with-Hurst, CNN-with-Hurst and GRU-with-Hurst. Empirical results show that the LSTM-with-Hurst and GRU-with-Hurst models achieve strong predictive performance, with training R 2 values of 0.9813 and 0.9812 and testing R 2 values of 0.8088 and 0.8022, respectively. In contrast, although the CNN-with-Hurst model performs well during training ( R 2 = 0.9869), its test performance is comparatively weaker ( R 2 = 0.9869) , indicating limited generalization. Overall, the findings demonstrate that integrating fractal features with recurrent deep learning architectures significantly enhances stock price forecasting accuracy, with LSTM-with-Hurst and GRU-with-Hurst emerging as robust and reliable tools for financial market prediction.