A Hybrid Approach to Stock Price Forecasting Using LSTM-ARO and Geometric Brownian Motion

Stock price prediction is a complex challenge due to high volatility, non-linearity, and external market influences. Traditional models struggle to capture intricate dependencies, while stochastic methods fail to adapt to evolving trends. To address this, we propose a hybrid approach integrating Long Short-Term Memory (LSTM) networks, Attention mechanisms, and Geometric Brownian Motion (GBM) for improved accuracy. The LSTM model, enhanced with an Attention-Enhanced Recurrent Optimization (ARO) layer, captures long-term dependencies, while GBM models price fluctuations using stochastic processes. By blending LSTM-ARO predictions with GBM trajectories, the framework leverages deep learning and probabilistic modeling for robustness. Evaluated on Microsoft (MSFT) stock data (2015–2025) with an 80-20 training-testing split, results show that the blended model achieves lower Mean Squared Error (MSE) than standalone LSTM-ARO and GBM models. Visualizations highlight its practical applicability. This research demonstrates the effectiveness of combining deep learning with stochastic methods to enhance financial time-series forecasting.