A Hybrid LSTM–Transformer Architecture with Bayesian Uncertainty Quantification for Multi-Horizon Financial Time Series Forecasting

This study introduces a novel Bayesian Temporal Fusion Transformer-LSTM Hybrid (B-TFTL) for multi-horizon financial time series forecasting, combining the sequence modeling strengths of LSTM with the contextual attention capabilities of Transformer architectures, augmented by Bayesian uncertainty quantification. The proposed algorithm integrates a probabilistic inference layer that captures predictive uncertainty through variational Bayesian techniques, enabling robust forecasting under noisy and non-stationary market conditions. Unlike conventional deterministic models, B-TFTL produces both point forecasts and confidence intervals, improving decision-making in risk-sensitive financial applications. The model is benchmarked against six widely used approaches: Autoregressive Integrated Moving Average (ARIMA), Generalized Autoregressive Conditional Heteroskedasticity (GARCH), standard LSTM, Gated Recurrent Unit (GRU), vanilla Transformer, and Temporal Fusion Transformer (TFT). Experimental results across equity indices, forex, and commodity datasets show that B-TFTL consistently outperforms these models in terms of lower root mean squared error (RMSE), improved directional accuracy, and better calibration of predictive intervals. The hybrid architecture effectively captures both short-term dependencies and long-range temporal patterns, while the Bayesian component enhances robustness to volatility clustering and structural shifts. Additionally, attention weight analysis provides interpretability by identifying key temporal features influencing forecasts. The proposed framework advances financial forecasting by unifying deep learning and probabilistic modeling, offering a powerful and reliable tool for multi-horizon prediction in complex financial environments.