TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting

TL;DR

TimeFilter tackles the challenge of dynamic, cross-variable dependencies in multivariate time-series forecasting by introducing patch-level graph filtration. It builds a Spatial-Temporal Construction graph on $n=C×N$ patches, uses a Patch-Specific Filtration (PSF) MoE router to selectively retain temporal, spatial, or spatial-temporal edges, and employs Adaptive Graph Learning (AGL) to refine the graph $M'$ for forecasting. The approach reduces noise from spurious correlations and delivers state-of-the-art results across 13 real-world datasets for both long- and short-term horizons, with robust performance and statistical significance against strong baselines. By enabling per-patch dependency tailoring and efficient parallel filtration, TimeFilter offers a scalable, generalizable solution for real-world time-series forecasting tasks.

Abstract

Time series forecasting methods generally fall into two main categories: Channel Independent (CI) and Channel Dependent (CD) strategies. While CI overlooks important covariate relationships, CD captures all dependencies without distinction, introducing noise and reducing generalization. Recent advances in Channel Clustering (CC) aim to refine dependency modeling by grouping channels with similar characteristics and applying tailored modeling techniques. However, coarse-grained clustering struggles to capture complex, time-varying interactions effectively. To address these challenges, we propose TimeFilter, a GNN-based framework for adaptive and fine-grained dependency modeling. After constructing the graph from the input sequence, TimeFilter refines the learned spatial-temporal dependencies by filtering out irrelevant correlations while preserving the most critical ones in a patch-specific manner. Extensive experiments on 13 real-world datasets from diverse application domains demonstrate the state-of-the-art performance of TimeFilter. The code is available at https://github.com/TROUBADOUR000/TimeFilter.

Figures (10)

• Figure 1: Analysis of three channels from the Electricity dataset shows the pros and cons of CI, CD, and CC strategies in different cases. Dynamic Time Warping (DTW) is a metric for measuring the similarity between two sequences, with lower values indicating higher similarity. The CI strategy ignores the highly correlated covariate information in the Supporting Case (left). The CD strategy fuses all information, including the irrelevant dependencies in the Supporting Case (right). The CC strategy addresses these issues by using global correlation to form CD and CI clusters. However, it cannot model the dynamic interactions of channels at different time steps at a fine-grained level. For example, in the Failure Case, it still faces the same dilemma as CD and CI strategies.
• Figure 2: The dependency map of $4$ different strategies. $t_i$ is the time step and $x_i$ is one channel. (a) CI strategy preserves only the temporal dependencies. (b) CD strategy fuses all dependencies. (c) Patch-wise Filtration finely selects dependencies for each patch. (d) Channel-wise Clustering coarsely models channel dependencies.
• Figure 3: The overall structure of TimeFilter, which consists of: (i) Spatial-Temporal Construction is devised to construct the spatial-temporal graph from the input $\mathbf{X}$; (ii) Patch-Specific Filtration facilitates spatial-temporal dependencies by filtering out irrelevant information for each patch; (iii) Adaptive Graph Learning is leveraged to predict the future $\mathbf{Y}$ based on GNN.
• Figure 4: Above are the dependencies learned by TimeFilter from the ETTh2, Weather and Electricity datasets. Below is the distribution of selected filters, where the x-axis represents the dependency types and the y-axis represents the number of different filters.
• Figure 5: Influence of look-back horizon. TimeFilter consistently outperforms other models under different look-back horizons.