Title: UniFy: Efficient Modeling of Non-Stationary Periodicity for Time Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Multivariate time series forecasting

Abstract: Periodic structures dominate long-term temporal dependencies in real-world signals, forming the cornerstone of long-term time series forecasting (LTSF). Existing methods typically aim to capture globally stable periodicity while overlooking the fact that real-world systems often exhibit substantial waveform variations across different periodic intervals. Representing such non-stationary sequences with a fixed period can lead to underfitting or overfitting of periodic components, thereby degrading forecasting accuracy. We further identify that the fundamental reason for this phenomenon is *frequency competition*, where multiple frequencies interfere with each other and distort the learning of periodic structures. We address this with a purely linear model: **Uni**fying Competing **F**requenc**y** (UniFy). It employs a multi-round Adaptive Frequency Selector (AFS) to progressively extract frequency components into multiple subspaces, mitigating frequency competition. Each subspace is then modeled by an Independent Linear Modeler (ILM) to extract its principal component, and the predictions from all subspaces are fused through Multi-subspace Calibration (MSC) to generate the final output. UniFy enables accurate and efficient modeling of non-stationary periodicity. Extensive experiments on 12 real-world datasets demonstrate the superiority of UniFy, delivering an average 16.0% MSE improvement on both long-term and short-term forecasting tasks, as well as an average 15.5% improvement in few-shot and zero-shot scenarios. Furthermore, its purely linear architecture ensures excellent computational efficiency and scalability. The code for our experiments is anonymously available at: https://anonymous.4open.science/r/UniFy-22F2/
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