BEAT: Balanced Frequency Adaptive Tuning for Long-Term Time-Series Forecasting

Accurate long-term time series forecasting (LTSF) requires the capture of complex long-range dependencies and dynamic periodic patterns. Recent advances in frequency-domain analysis offer a global perspective for uncovering temporal characteristics. However, real-world time series often exhibit pronounced cross-domain heterogeneity where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Existing frequency-based LTSF methods often rely on implicit assumptions of cross-domain homogeneity, which limits their ability to adapt to such intricate variability. To effectively integrate frequency-domain analysis with temporal dependency learning, we propose AdaMamba, a novel framework that endogenizes adaptive and context-aware frequency analysis within the Mamba state-space update process. Specifically, AdaMamba introduces an interactive patch encoding module to capture inter-variable interaction dynamics. Then, we develop an adaptive frequency-gated state-space module that generates input-dependent frequency bases, and generalizes the conventional temporal forgetting gate into a unified time-frequency forgetting gate. This allows dynamic calibration of state transitions based on learned frequency-domain importance, while preserving Mamba's capability in modeling long-range dependencies. Extensive experiments on seven public LTSF benchmarks and two domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art methods in forecasting accu racy while maintaining competitive computational efficiency. The code of AdaMamba is available at https://github.com/XDjiang25/AdaMamba.

Test-time adaptation (TTA) has recently emerged as a promising approach for improving time series forecasting (TSF) under distribution shift. Existing TSF-TTA methods differ in how they utilize revealed targets, yet the resulting adaptation protocols remain heterogeneous and lack a clearly unified formulation. To address this issue, we revisit TSF-TTA from the perspective of protocol cleanliness and propose an adaptation protocol based solely on matured ground truth, yielding a more principled setting for adaptation. Under this protocol, we further diagnose existing adapters in the frequency domain and find that their prediction corrections often exhibit limited and weakly structured spectral modifications. Motivated by this diagnosis, we propose Frequency-Aware Calibration (FAC), a lightweight calibration method that directly parameterizes prediction corrections in the frequency domain. Across diverse datasets, forecasting horizons, and source forecasters, FAC achieves competitive and consistent performance while requiring substantially fewer trainable parameters than the compared TSF-TTA adapters.

Long-term time-series forecasting needs models that are accurate yet efficient enough for commodity hardware. Lightweight linear forecasters are remarkably strong in this regime, yet they leave two openings: reversible instance normalization (RevIN) de-normalizes the entire horizon with a single lookback statistic, which is inaccurate under non-stationarity, and time-domain trend/seasonal decomposition relies on a fixed, non-adaptive filter. We present FreqLite, an ultra-lightweight, channel-independent frequency-decomposed linear forecaster: a learnable, lossless, partition-of-unity spectral filter splits the input into bands that are forecast by per-band linear heads and, unlike low-pass-truncation approaches, the high-frequency band is retained and modeled. FreqLite is the best lightweight model on the standard long-term forecasting benchmarks and, at long lookback (L=336), attains a lower average error than a PatchTST Transformer (0.3244 vs. 0.3587 MSE) while using 4x fewer parameters, 2.2x less memory, and 2.2x less time per epoch on a single 4 GB laptop GPU; although modest in magnitude, its improvements are statistically significant under paired Wilcoxon tests across all matched cells (p < 1e-5). We further introduce Adaptive Reversible Instance Normalization (A-RevIN), a regime-adaptive reversible normalization that strictly generalizes RevIN (recovered exactly when its gate is closed), engages under non-stationarity, and reduces to RevIN without harm on stationary data. We validate this on both a real strongly non-stationary dataset (ILI, up to ~5% MSE reduction) and a controlled synthetic drift sweep in which A-RevIN's benefit and its learned gate both rise monotonically with injected non-stationarity. Every component is independently ablatable (Linear and RLinear are special cases of FreqLite), and all results are reproducible on commodity hardware.