HRCformer: Hierarchical Recursive Convolution-Transformer with multi-scale Adaptive Recalibration for time series forecasting

Time series forecasting has significant applications across various domains, including industry, agriculture, and finance. Transformer-based models have shown significant promise in enhancing time series forecasting over the past few years. However, existing methods struggle to simultaneously capture local details and global semantics under single-view architectures. They also find it difficult to dynamically adapt to time-varying and multi-scale temporal patterns while accurately modeling the complex, time-varying relationships between multiple variables. To address these challenges, we propose HRCformer, a novel Transformer-based framework that introduces two key innovations: the Hierarchical Recursive Interaction Convolution (HRIC) and the Triad Adaptive Recalibration Module (TARM). HRIC achieves joint modeling of fine-grained short-term fluctuations and high-order cross-period dependencies in time series by integrating Divide-and-Process Convolution for local processing with Recursive Channel Interaction Convolution for global processing. TARM further enhances dynamic modeling via Dynamic Variance Attention, which amplifies critical temporal deviations through 3D attention, and the Adaptive Multivariate Recalibration, which uses a two-layer fully connected network with nonlinear activation to learn the dynamic relationships between channels, suppresses noise, and emphasizes informative multivariate interactions. Comprehensive experiments conducted on seven real-world datasets highlight the superiority of HRCformer compared to prior state-of-the-art methods.