HPMixer: Hierarchical Patching for Multivariate Time Series Forecasting

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.