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

arXiv: https://arxiv.org/abs/2609.24229 · HTML: https://mlsanity.com/paper/2609.24229/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)

## Abstract (arXiv)

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.