# Frequency Adaptive Normalization For Non-stationary Time Series Forecasting

arXiv: https://arxiv.org/abs/2409.20371 · HTML: https://mlsanity.com/paper/2409.20371/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [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)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks](https://mlsanity.com/paper/1701.05923/) (2017)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Domain Adaptation for Time Series Under Feature and Label Shifts](https://mlsanity.com/paper/2302.03133/) (2023)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [DDG-DA: Data Distribution Generation for Predictable Concept Drift Adaptation](https://mlsanity.com/paper/2201.04038/) (2022)
- [DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting](https://mlsanity.com/paper/2203.07681/) (2022)
- [Deep Frequency Derivative Learning for Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2407.00502/) (2024)

## Built on by (most cited first, 30 of 47)

- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2501.13989/) (2025)
- [Learning Robust Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2505.12585/) (2025)
- [FreqPolicy: Efficient Flow-based Visuomotor Policy via Frequency Consistency](https://mlsanity.com/paper/2506.08822/) (2025)
- [The Forecast After the Forecast: A Post-Processing Shift in Time Series](https://mlsanity.com/paper/2601.20280/) (2026)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [DeepFilter: A Transformer-style Framework for Accurate and Efficient Process Monitoring](https://mlsanity.com/paper/2501.01342/) (2025)
- [Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting](https://mlsanity.com/paper/2505.11781/) (2025)
- [Online time series prediction using feature adjustment](https://mlsanity.com/paper/2509.03810/) (2025)
- [Non-Stationary Time Series Forecasting Based on Fourier Analysis and Cross Attention Mechanism](https://mlsanity.com/paper/2505.06917/) (2025)
- [EventTSF: Event-Aware Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2508.13434/) (2025)
- [TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series](https://mlsanity.com/paper/2602.17122/) (2026)
- [On the Role of Reversible Instance Normalization](https://mlsanity.com/paper/2603.11869/) (2026)
- [PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2605.16793/) (2026)
- [ARIES: Relation Assessment and Model Recommendation for Deep Time Series Forecasting](https://mlsanity.com/paper/2509.06060/) (2025)
- [FreIE: Low-Frequency Spectral Bias in Neural Networks for Time-Series Tasks](https://mlsanity.com/paper/2510.25800/) (2025)
- [A Comparative Study on How Data Normalization Affects Zero-Shot Generalization in Time Series Foundation Models](https://mlsanity.com/paper/2512.02833/) (2025)
- [Test-Time Adaptation for Non-stationary Time Series: From Synthetic Regime Shifts to Financial Markets](https://mlsanity.com/paper/2602.00073/) (2026)
- [Revisiting the Seasonal Trend Decomposition for Enhanced Time Series Forecasting](https://mlsanity.com/paper/2602.18465/) (2026)
- [Rethinking Adam for Time Series Forecasting: A Simple Heuristic to Improve Optimization under Distribution Shifts](https://mlsanity.com/paper/2603.10095/) (2026)
- [FTimeXer: Frequency-aware Time-series Transformer with Exogenous variables for Robust Carbon Footprint Forecasting](https://mlsanity.com/paper/2604.02347/) (2026)
- [CANet: ChronoAdaptive Network for Enhanced Long-Term Time Series Forecasting under Non-Stationarity](https://mlsanity.com/paper/2504.17913/) (2025)
- [Multivariate Long-term Time Series Forecasting with Fourier Neural Filter](https://mlsanity.com/paper/2506.09174/) (2025)
- [DSAT-HD: Dual-Stream Adaptive Transformer with Hybrid Decomposition for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2509.24800/) (2025)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Autonomous Drift Learning in Data Streams: A Unified Perspective](https://mlsanity.com/paper/2605.01295/) (2026)
- [STEPS: A Temporal Smooth Error Propagation Solver on the Manifolds for Test-Time Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2605.08005/) (2026)
- [NoRIN: Backbone-Adaptive Reversible Normalization for Time-Series Forecasting](https://mlsanity.com/paper/2605.10823/) (2026)
- [SeesawNet: Towards Non-stationary Time Series Forecasting with Balanced Modeling of Common and Specific Dependencies](https://mlsanity.com/paper/2605.14551/) (2026)

## Abstract (arXiv)

Time series forecasting typically needs to address non-stationary data with evolving trend and seasonal patterns. To address the non-stationarity, reversible instance normalization has been recently proposed to alleviate impacts from the trend with certain statistical measures, e.g., mean and variance. Although they demonstrate improved predictive accuracy, they are limited to expressing basic trends and are incapable of handling seasonal patterns. To address this limitation, this paper proposes a new instance normalization solution, called frequency adaptive normalization (FAN), which extends instance normalization in handling both dynamic trend and seasonal patterns. Specifically, we employ the Fourier transform to identify instance-wise predominant frequent components that cover most non-stationary factors. Furthermore, the discrepancy of those frequency components between inputs and outputs is explicitly modeled as a prediction task with a simple MLP model. FAN is a model-agnostic method that can be applied to arbitrary predictive backbones. We instantiate FAN on four widely used forecasting models as the backbone and evaluate their prediction performance improvements on eight benchmark datasets. FAN demonstrates significant performance advancement, achieving 7.76% ~ 37.90% average improvements in MSE.