HDMixer: Hierarchical Dependency with Extendable Patch for Multivariate Time Series Forecasting

Abstract Multivariate time series (MTS) prediction has been widely adopted in various scenarios. Recently, some methods have employed patching to enhance local semantics and improve model performance. However, length-fixed patch are prone to losing temporal boundary information, such as complete peaks and periods. Moreover, existing methods mainly focus on modeling long-term dependencies across patches, while paying little attention to other dimensions (e.g., short-term dependencies within patches and complex interactions among cross-variavle patches). To address these challenges, we propose a pure MLP-based HDMixer, aiming to acquire patches with richer semantic information and efficiently modeling hierarchical interactions. Specifically, we design a Length-Extendable Patcher (LEP) tailored to MTS, which enriches the boundary information of patches and alleviates semantic incoherence in series. Subsequently, we devise a Hierarchical Dependency Explorer (HDE) based on pure MLPs. This explorer effectively models short-term dependencies within patches, long-term dependencies across patches, and complex interactions among variables. Extensive experiments on 9 real-world datasets demonstrate the superiority of our approach. The code is available at https://github.com/hqh0728/HDMixer.