Financial time series forecasting with a hybrid VMD–CSA–BiT framework

Financial time series forecasting faces significant challenges due to inherent nonlinearity, non-stationarity, and high levels of noise. To address these issues, this study proposes VMD-CSA-BiT, an integrated framework that combines variational mode decomposition (VMD), convolutional self-attention (CSA), and bidirectional transformers (BiT) to enhance prediction robustness. The methodology first decomposes raw price series into interpretable intrinsic mode functions via VMD. It then employs the CSA module to refine pointwise representations at individual time steps and applies the BiT network to model bidirectional long-term temporal dependencies. Evaluated on a range of financial assets using a comprehensive set of market features, the proposed framework demonstrates consistent performance improvements over multiple benchmark models, including traditional statistical methods, machine learning models, and advanced deep learning architectures, achieving significant reductions in key error metrics. The results indicate that VMD-CSA-BiT offers superior forecasting accuracy and stability, with visual analyses showing that its predictions generally align with actual market movements. This study shows that VMD-CSA-BiT is a promising and effective approach for financial time series forecasting. Future research will focus on further architectural optimizations and extending the framework to additional financial applications.