# Non-Stationary Time Series Forecasting Based on Fourier Analysis and Cross Attention Mechanism

arXiv: https://arxiv.org/abs/2505.06917 · HTML: https://mlsanity.com/paper/2505.06917/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 11 May 2025.

## Builds on (most cited first, 23 of 23)

- [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)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (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)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [A Comparative Study on Transformer vs RNN in Speech Applications](https://mlsanity.com/paper/1909.06317/) (2019)
- [ETSformer: Exponential Smoothing Transformers for Time-series Forecasting](https://mlsanity.com/paper/2202.01381/) (2022)
- [AMMUS : A Survey of Transformer-based Pretrained Models in Natural Language Processing](https://mlsanity.com/paper/2108.05542/) (2021)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Cross-Attention is All You Need: Adapting Pretrained Transformers for Machine Translation](https://mlsanity.com/paper/2104.08771/) (2021)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [DDG-DA: Data Distribution Generation for Predictable Concept Drift Adaptation](https://mlsanity.com/paper/2201.04038/) (2022)
- [T-WaveNet: Tree-Structured Wavelet Neural Network for Sensor-Based Time Series Analysis](https://mlsanity.com/paper/2012.05456/) (2020)

## Built on by (most cited first, 2 of 2)

- [Graph-Based Uncertainty Modeling and Multimodal Fusion for Salient Object Detection](https://mlsanity.com/paper/2508.20415/) (2025)
- [Adaptive Normalization Mamba with Multi Scale Trend Decomposition and Patch MoE Encoding](https://mlsanity.com/paper/2512.06929/) (2025)

## Abstract (arXiv)

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot effectively capture the statistical characteristics that change over time. To address this problem, this paper proposes a new framework, AEFIN, which enhances the information sharing ability between stable and unstable components by introducing a cross-attention mechanism, and combines Fourier analysis networks with MLP to deeply explore the seasonal patterns and trend characteristics in unstable components. In addition, we design a new loss function that combines time-domain stability constraints, time-domain instability constraints, and frequency-domain stability constraints to improve the accuracy and robustness of forecasting. Experimental results show that AEFIN outperforms the most common models in terms of mean square error and mean absolute error, especially under non-stationary data conditions, and shows excellent forecasting capabilities. This paper provides an innovative solution for the modeling and forecasting of non-stationary time series data, and contributes to the research of deep learning for complex time series.