# Not All Frequencies Are Created Equal:Towards a Dynamic Fusion of Frequencies in Time-Series Forecasting

arXiv: https://arxiv.org/abs/2407.12415 · HTML: https://mlsanity.com/paper/2407.12415/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 73 references that are in the map.
- First posted on arXiv 17 Jul 2024.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [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)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [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)
- [Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency](https://mlsanity.com/paper/2206.08496/) (2022)
- [Representation Learning via Invariant Causal Mechanisms](https://mlsanity.com/paper/2010.07922/) (2020)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [FcaNet: Frequency Channel Attention Networks](https://mlsanity.com/paper/2012.11879/) (2020)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Filter-enhanced MLP is All You Need for Sequential Recommendation](https://mlsanity.com/paper/2202.13556/) (2022)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [Spatio-Temporal Branching for Motion Prediction using Motion Increments](https://mlsanity.com/paper/2308.01097/) (2023)
- [Infomaxformer: Maximum Entropy Transformer for Long Time-Series Forecasting Problem](https://mlsanity.com/paper/2301.01772/) (2023)
- [Does Long-Term Series Forecasting Need Complex Attention and Extra Long Inputs?](https://mlsanity.com/paper/2306.05035/) (2023)
- [GCformer: An Efficient Framework for Accurate and Scalable Long-Term Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.08325/) (2023)
- [Enhancing Representation Learning for Periodic Time Series with Floss: A Frequency Domain Regularization Approach](https://mlsanity.com/paper/2308.01011/) (2023)
- [Comparative Analysis of Time Series Forecasting Approaches for Household Electricity Consumption Prediction](https://mlsanity.com/paper/2207.01019/) (2022)

## Built on by (most cited first, 6 of 6)

- [DeepFilter: A Transformer-style Framework for Accurate and Efficient Process Monitoring](https://mlsanity.com/paper/2501.01342/) (2025)
- [TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series](https://mlsanity.com/paper/2602.17122/) (2026)
- [Beyond All-to-All: Causal-Aligned Transformer with Dynamic Structure Learning for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.16308/) (2025)
- [Fewer yet critical: Reducing Redundant Token Dependencies for Transformer-based Time Series Forecasting](https://mlsanity.com/paper/2503.06867/) (2025)
- [Dualformer: Time-Frequency Dual Domain Learning for Long-term Time Series Forecasting](https://mlsanity.com/paper/2601.15669/) (2026)
- [Dirichlet-Guided Group Forecasting for Alleviating Over-smoothing in Time Series Forecasting](https://mlsanity.com/paper/2606.10592/) (2026)

## Abstract (arXiv)

Long-term time series forecasting is a long-standing challenge in various applications. A central issue in time series forecasting is that methods should expressively capture long-term dependency. Furthermore, time series forecasting methods should be flexible when applied to different scenarios. Although Fourier analysis offers an alternative to effectively capture reusable and periodic patterns to achieve long-term forecasting in different scenarios, existing methods often assume high-frequency components represent noise and should be discarded in time series forecasting. However, we conduct a series of motivation experiments and discover that the role of certain frequencies varies depending on the scenarios. In some scenarios, removing high-frequency components from the original time series can improve the forecasting performance, while in others scenarios, removing them is harmful to forecasting performance. Therefore, it is necessary to treat the frequencies differently according to specific scenarios. To achieve this, we first reformulate the time series forecasting problem as learning a transfer function of each frequency in the Fourier domain. Further, we design Frequency Dynamic Fusion (FreDF), which individually predicts each Fourier component, and dynamically fuses the output of different frequencies. Moreover, we provide a novel insight into the generalization ability of time series forecasting and propose the generalization bound of time series forecasting. Then we prove FreDF has a lower bound, indicating that FreDF has better generalization ability. Extensive experiments conducted on multiple benchmark datasets and ablation studies demonstrate the effectiveness of FreDF. The code is available at https://github.com/Zh-XY22/FreDF.