# Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks

arXiv: https://arxiv.org/abs/2504.07099 · HTML: https://mlsanity.com/paper/2504.07099/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 182 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 30 of 60)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [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)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [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)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Less Is More: Fast Multivariate Time Series Forecasting with Light Sampling-oriented MLP Structures](https://mlsanity.com/paper/2207.01186/) (2022)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Multivariate LSTM-FCNs for Time Series Classification](https://mlsanity.com/paper/1801.04503/) (2018)
- [Large Language Models for Time Series: A Survey](https://mlsanity.com/paper/2402.01801/) (2024)
- [TSLANet: Rethinking Transformers for Time Series Representation Learning](https://mlsanity.com/paper/2404.08472/) (2024)
- [RobustSTL: A Robust Seasonal-Trend Decomposition Algorithm for Long Time Series](https://mlsanity.com/paper/1812.01767/) (2018)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)

## Built on by (most cited first, 10 of 10)

- [FLDmamba: Integrating Fourier and Laplace Transform Decomposition with Mamba for Enhanced Time Series Prediction](https://mlsanity.com/paper/2507.12803/) (2025)
- [MODE: Efficient Time Series Prediction with Mamba Enhanced by Low-Rank Neural ODEs](https://mlsanity.com/paper/2601.00920/) (2026)
- [StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser](https://mlsanity.com/paper/2603.00037/) (2026)
- [L-Drive: Beyond a Single Mapping-Latent Context Drives Time Series Forecasting](https://mlsanity.com/paper/2605.17730/) (2026)
- [FAIM: Frequency-Aware Interactive Mamba for Time Series Classification](https://mlsanity.com/paper/2512.07858/) (2025)
- [MLOW: Interpretable Low-Rank Frequency Magnitude Decomposition of Multiple Effects for Time Series Forecasting](https://mlsanity.com/paper/2603.18432/) (2026)
- [DySCo: Dynamic Semantic Compression for Effective Long-term Time Series Forecasting](https://mlsanity.com/paper/2604.01261/) (2026)
- [Frequency-aware decomposition learning for sensorless wrench estimation in vibration-rich robotic contact](https://mlsanity.com/paper/2604.12905/) (2026)
- [Beyond Uniform Tokens: Adaptive Compression for Time Series Language Models](https://mlsanity.com/paper/2606.13624/) (2026)
- [DecoVAE: a Lightweight Interpretable Trend-Seasonal VAE Framework for Efficient Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2608.20052/) (2026)

## Abstract (arXiv)

Frequency-domain analysis has emerged as a powerful paradigm for time series analysis, offering unique advantages over traditional time-domain approaches while introducing new theoretical and practical challenges. This survey provides a comprehensive examination of spectral methods from classical Fourier analysis to modern neural operators, systematically summarizing three open challenges in current research: (1) causal structure preservation during spectral transformations, (2) uncertainty quantification in learned frequency representations, and (3) topology-aware analysis for non-Euclidean data structures. Through rigorous reviewing of over 100 studies, we develop a unified taxonomy that bridges conventional spectral techniques with cutting-edge machine learning approaches, while establishing standardized benchmarks for performance evaluation. Our work identifies key knowledge gaps in the field, particularly in geometric deep learning and quantum-enhanced spectral analysis. The survey offers practitioners a systematic framework for method selection and implementation, while charting promising directions for future research in this rapidly evolving domain.