Towards Non-Stationary Time Series Forecasting with Temporal Stabilization and Frequency Differencing

TL;DR

This work tackles non-stationarity in time series forecasting by introducing DTAF, a dual-branch architecture that handles temporal non-stationarity with Temporal Stabilizing Fusion (TFS) and spectral non-stationarity with Frequency Wave Modeling (FWM). A Dual-branch Attention module fuses the temporal and spectral representations to produce robust forecasts. Extensive experiments across 11 real-world datasets demonstrate state-of-the-art accuracy, with notable gains on non-stationary tasks like Covid-19 and NN5, and ablations confirm that both branches and the attention fusion contribute significantly. The methodology advances non-stationary time-series modeling by jointly addressing shifts in time and frequency domains and provides a practical, reproducible framework with available code.

Abstract

Time series forecasting is critical for decision-making across dynamic domains such as energy, finance, transportation, and cloud computing. However, real-world time series often exhibit non-stationarity, including temporal distribution shifts and spectral variability, which pose significant challenges for long-term time series forecasting. In this paper, we propose DTAF, a dual-branch framework that addresses non-stationarity in both the temporal and frequency domains. For the temporal domain, the Temporal Stabilizing Fusion (TFS) module employs a non-stationary mix of experts (MOE) filter to disentangle and suppress temporal non-stationary patterns while preserving long-term dependencies. For the frequency domain, the Frequency Wave Modeling (FWM) module applies frequency differencing to dynamically highlight components with significant spectral shifts. By fusing the complementary outputs of TFS and FWM, DTAF generates robust forecasts that adapt to both temporal and frequency domain non-stationarity. Extensive experiments on real-world benchmarks demonstrate that DTAF outperforms state-of-the-art baselines, yielding significant improvements in forecasting accuracy under non-stationary conditions. All codes are available at https://github.com/decisionintelligence/DTAF.

Figures (6)

• Figure 1: A non-stationary time series split into four patches (A, B, C, D), (b-e) shows the amplitude spectrum of the four patches, (f-i) shows diverse distributions in the temporal domain, and (j-m) shows diverse distributions in the frequency domain, reflecting non-stationarity across both domains.
• Figure 2: The architecture of DTAF. The two main components of DTAF are TFS and FWM. They are used to aggregate the information in the temporal domain and model in the frequency domain with differencing. Temporal aggregation captures long-term dependencies and local variations, while frequency differencing provides insights into the changing spectral components.
• Figure 3: The weights of different experts for the ETTh1. P1, P2, P3, and P4 denote four patches from the sequence, while E1, E2, E3, and E4 represent four experts to extract non-stationary patterns.
• Figure 4: Non-stationary MOE Filter Analysis.
• Figure 5: TopK selection Analysis.