HPMixer: Hierarchical Patching for Multivariate Time Series Forecasting

Jung Min Choi; Vijaya Krishna Yalavarthi; Lars Schmidt-Thieme

cs.LGFeb 18, 2026

HPMixer: Hierarchical Patching for Multivariate Time Series Forecasting

Authors: Jung Min Choi, Vijaya Krishna Yalavarthi, Lars Schmidt-Thieme

Organizations: ISMLL, University of Hildesheim

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.

Figures & tables

Figure 1: An overview of the proposed model HPMixer architecture.

Figure 2: Autocorrelation (ACF) plots for three channels of the ETTm2 dataset. The first channel (ETTm2[0]) exhibits a clear periodic signal with noticeable peaks every 96 time steps, whereas the third channel (ETTm2[3]) shows a weaker and less regular periodic pattern. The fifth channel (ETTm2[5]) displays only very vague cyclic structure at the 96-step frequency.

Figure 3: Architecture of the Learnable Mixing Cycle Module , the Channel-Mixing Encoder , and Coarse-Fine Patching Mixer .

Model	ETTm1		ETTh1		Weather		ECL
	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
w/o MLP in Mixing Cycle Module	0.365	0.388	0.442	0.438	0.248	0.275	0.166	0.262
w/o Mixing Cycle Module	0.406	0.414	0.437	0.434	0.247	0.277	0.184	0.278
w/o trainable SWT	0.417	0.421	0.426	0.431	0.247	0.277	0.162	0.258
w/o SWT	0.439	0.43	0.455	0.447	0.247	0.276	0.163	0.26
One-level Patching	0.39	0.402	0.439	0.44	0.247	0.276	0.164	0.262

Table 2: Ablation study results on multiple datasets. Lower MSE and MAE indicate better performance. Hyperparameters were independently optimized for each ablation setting.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Statistics		Dataset Split
Dataset	$C$	$T$	( $N_{\text{train}},N_{\text{val}},N_{\text{test}}$ )
ETTh1 [ 21 ]	7	17,420	(8,545, 2,881, 2,881)
ETTh2 [ 21 ]	7	17,420	(8,545, 2,881, 2,881)
ETTm1 [ 21 ]	7	69,680	(34,465, 11,521, 11,521)
ETTm2 [ 21 ]	7	69,680	(34,465, 11,521, 11,521)
Weather [ 17 ]	21	52,696	(36,792, 5,271, 10,540)

Appendix

Table 3: Summary of dataset statistics and experimental configurations.

Hyperparameter	Search Space / Values
Learning Rate	Float $\in[10^{-4},10^{-2}]$ (Log-scale)
$d_{\text{model}}$	$\{32,64,128,256,512,1024\}$
$d_{\text{ff}}$	$\{32,64,128,256,512,1024,2048\}$
Dropout	Float $\in[0.4,0.9]$
Encoder Layers ( $e_{\text{layers}}$ )	Integer $\in[1,5]$
FC Dropout	$\{0,0.1,0.2\}$

Appendix

Table 4: Hyperparameter search space explored using Optuna.

Dataset	Model	MSE $\downarrow$	Total Params	GFLOPs	Speed (s/iter) $\downarrow$
Weather	HPMixer (Ours)	0.154	172,172	0.1741	0.1364
	SimpleTM	0.162	14,880	0.0099	0.2424
ETTm1	HPMixer (Ours)	0.305	5,324,504	0.9802	0.2488
	SimpleTM	0.321	1,700,576	0.7611	0.4210

Appendix

Table 5: Efficiency Analysis: Comparison of HPMixer (Ours) and SimpleTM across Weather and ETTm1 datasets (

L=96,T=96

Figure 4: Robustness analysis evaluating the impact of varying patch sizes and cycle lengths on the ECL and ETTm1 datasets. The original optimal configurations are marked to demonstrate their superiority in minimizing the Mean Squared Error.

Figure 5: Visual verification of the decoupling mechanism on the Electricity (top) and ETTm1 (bottom) datasets. The architecture successfully isolates the core cyclical structure (middle panels) from the non-periodic, high-frequency residuals and stochastic deviations (bottom panels).

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NPMixer: Hierarchical Neighboring Patch Mixing for Time Series Forecasting

Jung Min Choi, Vijaya Krishna Yalavarthi, Lars Schmidt-Thieme

1ISMLL, University of Hildesheim, VWFS Data Analytics Research Center (VWFS-DARC), Hildesheim, Germany.

Multivariate Time Series Forecasting Time Series Forecasting Wavelet Methods Time Series Decomposition Multiscale Time-Series Modeling

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Multivariate time series forecasting remains a challenge due to the complexity of local temporal dynamics and global dependencies across multiple variables. In this paper, we propose Neighboring Patching Mixer (NPMixer), a hierarchical architecture featuring a Learnable Stationary Wavelet Transform that adaptively learns filter coefficients to decompose signals into trend and detail components in a data-dependent manner. Our framework introduces a Neighboring Mixer Block that captures local temporal dynamics through a series of hierarchical MLP layers operating on non-overlapping patches. Specifically, the mixer block utilizes MLPs to learn temporal patterns within and across these patches, expanding the receptive field to capture multi-scale dependencies. A Channel-Mixing Encoder is applied to high-frequency components to learn channel correlations while preserving the stability of the underlying global trend. Extensive experiments on seven benchmark datasets demonstrate that NPMixer consistently outperforms state-of-the-art models, achieving better performance in 20 out of 28 (

71.4\%

) evaluated experimental setups for MSE.

Abstract

Multivariate Time Series Forecasting

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