# FreDF: Learning to Forecast in the Frequency Domain

arXiv: https://arxiv.org/abs/2402.02399 · HTML: https://mlsanity.com/paper/2402.02399/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [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)
- [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)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (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)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [Scaleformer: Iterative Multi-scale Refining Transformers for Time Series Forecasting](https://mlsanity.com/paper/2206.04038/) (2022)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [Entire Space Counterfactual Learning for Reliable Content Recommendations](https://mlsanity.com/paper/2210.11039/) (2022)
- [Double machine learning for sample selection models](https://mlsanity.com/paper/2012.00745/) (2020)
- [Towards Better Long-range Time Series Forecasting using Generative Forecasting](https://mlsanity.com/paper/2212.06142/) (2022)

## Built on by (most cited first, 30 of 79)

- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [TAB: Unified Benchmarking of Time Series Anomaly Detection Methods](https://mlsanity.com/paper/2506.18046/) (2025)
- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain](https://mlsanity.com/paper/2505.08550/) (2025)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [Bridging Past and Future: Distribution-Aware Alignment for Time Series Forecasting](https://mlsanity.com/paper/2509.14181/) (2025)
- [FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2501.13989/) (2025)
- [PPGF: Probability Pattern-Guided Time Series Forecasting](https://mlsanity.com/paper/2502.12802/) (2025)
- [Accurate Parameter-Efficient Test-Time Adaptation for Time Series Forecasting](https://mlsanity.com/paper/2506.23424/) (2025)
- [DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment](https://mlsanity.com/paper/2510.24574/) (2025)
- [GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2603.08032/) (2026)
- [TimeMosaic: Temporal Heterogeneity Guided Time Series Forecasting via Adaptive Granularity Patch and Segment-wise Decoding](https://mlsanity.com/paper/2509.19406/) (2025)
- [VLANeXt: Recipes for Building Strong VLA Models](https://mlsanity.com/paper/2602.18532/) (2026)
- [FreCT: Frequency-augmented Convolutional Transformer for Robust Time Series Anomaly Detection](https://mlsanity.com/paper/2505.00941/) (2025)
- [Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models](https://mlsanity.com/paper/2511.00053/) (2025)
- [ASTGI: Adaptive Spatio-Temporal Graph Interactions for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2509.23313/) (2025)
- [Selective Learning for Deep Time Series Forecasting](https://mlsanity.com/paper/2510.25207/) (2025)
- [Modeling Temporal Dependencies within the Target for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2406.04777/) (2024)
- [From Observations to States: Latent Time Series Forecasting](https://mlsanity.com/paper/2602.00297/) (2026)
- [DeepFilter: A Transformer-style Framework for Accurate and Efficient Process Monitoring](https://mlsanity.com/paper/2501.01342/) (2025)
- [Unlocking the Value of Text: Event-Driven Reasoning and Multi-Level Alignment for Time Series Forecasting](https://mlsanity.com/paper/2603.15452/) (2026)
- [FTMixer: Frequency and Time Domain Representations Fusion for Time Series Modeling](https://mlsanity.com/paper/2405.15256/) (2024)
- [Disentangled Parameter-Efficient Linear Model for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2411.17257/) (2024)
- [Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting](https://mlsanity.com/paper/2505.11781/) (2025)
- [Beyond Magnitude and Shape: A Direction-Aware Loss for Time Series Forecasting](https://mlsanity.com/paper/2608.01857/) (2026)
- [KANMixer: a minimal KAN-centered mixer for long-term time series forecasting](https://mlsanity.com/paper/2508.01575/) (2025)
- [TimeSense:Making Large Language Models Proficient in Time-Series Analysis](https://mlsanity.com/paper/2511.06344/) (2025)
- [FreDN: Spectral Disentanglement for Time Series Forecasting via Learnable Frequency Decomposition](https://mlsanity.com/paper/2511.11817/) (2025)

## Abstract (arXiv)

Time series modeling presents unique challenges due to autocorrelation in both historical data and future sequences. While current research predominantly addresses autocorrelation within historical data, the correlations among future labels are often overlooked. Specifically, modern forecasting models primarily adhere to the Direct Forecast (DF) paradigm, generating multi-step forecasts independently and disregarding label autocorrelation over time. In this work, we demonstrate that the learning objective of DF is biased in the presence of label autocorrelation. To address this issue, we propose the Frequency-enhanced Direct Forecast (FreDF), which mitigates label autocorrelation by learning to forecast in the frequency domain, thereby reducing estimation bias. Our experiments show that FreDF significantly outperforms existing state-of-the-art methods and is compatible with a variety of forecast models. Code is available at https://github.com/Master-PLC/FreDF.