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.
Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.
Recent advances in Large Language Models (LLMs) have spurred cross-modal solutions for time-series forecasting. However, existing methods rely heavily on textual prompts for modality alignment-introducing nontrivial computational overhead and failing to leverage the rich spectral dynamics inherent in time-series data. To enable prompt-free, frequency-aware adaptation of frozen LLMs, we propose FM-LLM (Frequency-Enhanced Mixture-of-Experts for adapting LLMs to Time Series Forecasting), an autoregressive framework grounded in constrained asymmetric coupling. A Fourier Analysis Network (FAN)-based spectral token aligner injects structured harmonic representations directly into the frozen LLM with numerical compatibility. An asymmetric Mixture-of-Experts (MoE) decoder enforces role separation: shared experts with lightweight FAN layers reconstruct the global periodic backbone, while routed experts-restricted to standard FFNs-specialize in modeling non-periodic residual dynamics. A time-frequency hybrid loss function jointly optimizes temporal accuracy and spectral consistency, mitigating error accumulation during long-horizon autoregressive rollouts. Evaluated across eleven public benchmarks, FM-LLM achieves state-of-the-art performance on 59 out of 78 evaluation metrics. Compared to the strongest autoregressive LLM-based baseline, it delivers average improvements of 5.3% in MSE and 5.6% in MAE, with maximum gains reaching 8.0% for MSE and 8.4% for MAE. FM-LLM also demonstrates robust transferability, maintaining superior performance in 10% few-shot and zero-shot forecasting scenarios.
Long-term time series forecasting finds extensive applications in domains such as power demand, traffic flow, meteorological observation, and renewable energy dispatch. Forecasting dynamically varying long-term time series poses inherent challenges, including statistical nonstationarity, local high-frequency disturbances, and coupled cross-period dependencies, which make it difficult for lightweight models to balance parameter efficiency and forecasting performance. To address this issue, this study presents TA-SparseMG, a lightweight cross-period forecasting model built on SparseTSF's sparse cross-period modeling framework. It incorporates three key modules: a trend-aware reversible instance normalization module, a scale-adaptive gated denoising module, and a multiscale gated-attention MLP forecasting module. The trend-aware normalization module captures input-window statistics and calibrates forecast-window distributions, effectively mitigating distribution shift. The scale-adaptive gated denoising module performs feature smoothing and residual suppression before period rearrangement, thereby reducing interference from high-frequency perturbations. The multiscale gated attention prediction module strengthens the prediction head's adaptive representational capacity via conditional gating and feature modulation. Extensive experiments across multiple LTSF benchmarks demonstrate that the proposed TA-SparseMG consistently achieves superior, stable performance. Ablation studies confirm that each module independently improves distribution adaptation, input robustness, and cross-period feature mapping capability.