@article{Wang2026, 
author = {Qi Wang and Kelvin Amos Nicodemas},
title = {Hierarchical Attention Transformer for Multivariate Time Series Forecasting},
year = {2026},
journal = {Computers, Materials & Continua},
volume = {87},
number = {2},
pages = {78},
keywords = {Time series forecasting, multi-scale temporal modeling, cross-scale attention, transformer architecture, hierarchical embeddings, gradient flow optimization},
url = {https://www.sciopen.com/article/10.32604/cmc.2026.074305},
doi = {10.32604/cmc.2026.074305},
abstract = {Multivariate time series forecasting plays a crucial role in decision-making for systems like energy grids and transportation networks, where temporal patterns emerge across diverse scales from short-term fluctuations to long-term trends. However, existing Transformer-based methods often process data at a single resolution or handle multiple scales independently, overlooking critical cross-scale interactions that influence prediction accuracy. To address this gap, we introduce the Hierarchical Attention Transformer (HAT), which enables direct information exchange between temporal hierarchies through a novel cross-scale attention mechanism. HAT extracts multi-scale features using hierarchical convolutional-recurrent blocks, fuses them via temperature-controlled mechanisms, and optimizes gradient flow with residual connections for stable training. Evaluations on eight benchmark datasets show HAT outperforming state-of-the-art baselines, with average reductions of 8.2% in MSE and 7.5% in MAE across horizons, while achieving a  6.1× training speedup over patch-based methods. These advancements highlight HAT’s potential for applications requiring multi-resolution temporal modeling.}
}