Runmin Zou | Search arXiv

arXiv2026

Recovering Lost Details: Multi-Scale Frequency Compensation for Long-Term Time Series Forecasting

Long-term time series forecasting has made significant progress by leveraging multi-scale information to capture hierarchical temporal patterns and model long-range dependencies. However, temporal downsampling in existing multi-scale methods inevitably smooths detailed temporal fluctuations, and this information loss is further aggravated by their emphasis on dominant trends across scales, resulting in insufficiently expressive representations. To address this, we propose a Multi-Scale Wavelet Mixing (MWMixer) model, which incorporates a Bidirectional Frequency-Bands Mixing strategy to recover lost temporal details across scales, enabling complementary cross-scale information interactions. Then, a Dynamic Scale-Adaptive Fusion module learns time-varying weights for each scale to fuse multi-scale forecasts into the final prediction, enhancing the flexibility of multi-scale aggregation. In addition, a cross-scale consistency loss aligns each coarse-scale prediction with the interval-averaged fine-scale outputs, while a multi-scale supervision loss enforces prediction accuracy at each scale, promoting consistent learning across scales. Extensive experiments on seven real-world datasets demonstrate that MWMixer achieves competitive performance in long-term forecasting.

cs.AI↗

arXiv2026

M$^2$FMoE: Multi-Resolution Multi-View Frequency Mixture-of-Experts for Extreme-Adaptive Time Series Forecasting

Forecasting time series with extreme events is critical yet challenging due to their high variance, irregular dynamics, and sparse but high-impact nature. While existing methods excel in modeling dominant regular patterns, their performance degrades significantly during extreme events, constituting the primary source of forecasting errors in real-world applications. Although some approaches incorporate auxiliary signals to improve performance, they still fail to capture extreme events' complex temporal dynamics. To address these limitations, we propose M$^2$FMoE, an extreme-adaptive forecasting model that learns both regular and extreme patterns through multi-resolution and multi-view frequency modeling. It comprises three modules: (1) a multi-view frequency mixture-of-experts module assigns experts to distinct spectral bands in Fourier and Wavelet domains, with cross-view shared band splitter aligning frequency partitions and enabling inter-expert collaboration to capture both dominant and rare fluctuations; (2) a multi-resolution adaptive fusion module that hierarchically aggregates frequency features from coarse to fine resolutions, enhancing sensitivity to both short-term variations and sudden changes; (3) a temporal gating integration module that dynamically balances long-term trends and short-term frequency-aware features, improving adaptability to both regular and extreme temporal patterns. Experiments on real-world hydrological datasets with extreme patterns demonstrate that M$^2$FMoE outperforms state-of-the-art baselines without requiring extreme-event labels.

cs.LG↗