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.

翻译：在长期多元时间序列预测中，有效捕捉周期性模式与残差动态至关重要。为在标准深度学习基准设置下解决此问题，我们提出分层分块混合模型（HPMixer），以解耦但互补的方式对周期性与残差进行建模。周期性组件采用可学习周期模块[7]，并通过非线性通道级MLP增强其表达能力。残差组件通过可学习平稳小波变换（LSWT）进行处理，以提取稳定、平移不变的频域表示。随后，通道混合编码器显式建模通道间依赖关系，而两级非重叠分层分块机制则捕捉粗粒度与细粒度的残差变化。通过将解耦的周期性建模与结构化多尺度残差学习相结合，HPMixer提供了一个有效的框架。在标准多元基准上的大量实验表明，相较于近期基线模型，HPMixer取得了具有竞争力或最先进的性能。