HPMixer: Hierarchical Patching for Multivariate Time Series Forecasting

2026-02-18

AI Summary

This work addresses the challenge of jointly modeling periodic patterns and residual dynamics in long-term multivariate time series forecasting. To this end, it proposes a decoupled yet complementary modeling paradigm: periodic components are captured through a learnable recurrent module combined with channel-wise nonlinear MLPs, while residual components are represented by extracting frequency-domain features via a learnable stationary wavelet transform (LSWT). These residuals are further processed using a channel-mixing encoder and a two-level non-overlapping hierarchical patch mechanism to effectively capture multiscale temporal dynamics. Evaluated on standard multivariate time series benchmarks, the proposed method achieves state-of-the-art or competitive performance, significantly improving long-horizon prediction accuracy.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Multi-modal Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

Abstract

In long-term multivariate time series forecasting, effectively capturing both periodic patterns and residual dynamics is essential. To address this within standard deep learning benchmark settings, we propose the Hierarchical Patching Mixer (HPMixer), which models periodicity and residuals in a decoupled yet complementary manner. The periodic component utilizes a learnable cycle module [7] enhanced with a nonlinear channel-wise MLP for greater expressiveness. The residual component is processed through a Learnable Stationary Wavelet Transform (LSWT) to extract stable, shift-invariant frequency-domain representations. Subsequently, a channel-mixing encoder models explicit inter-channel dependencies, while a two-level non-overlapping hierarchical patching mechanism captures coarse- and fine-scale residual variations. By integrating decoupled periodicity modeling with structured, multi-scale residual learning, HPMixer provides an effective framework. Extensive experiments on standard multivariate benchmarks demonstrate that HPMixer achieves competitive or state-of-the-art performance compared to recent baselines.

Problem

• multivariate time series forecasting
• periodicity modeling
• residual dynamics
• long-term forecasting

Innovation

• Hierarchical Patching
• Learnable Stationary Wavelet Transform
• Decoupled Periodicity Modeling
• Channel-wise MLP
• Multiscale Residual Learning