# Deep Frequency Derivative Learning for Non-stationary Time Series Forecasting

arXiv: https://arxiv.org/abs/2407.00502 · HTML: https://mlsanity.com/paper/2407.00502/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 29 Jun 2024.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [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)
- [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)
- [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)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting](https://mlsanity.com/paper/2203.07681/) (2022)
- [AutoFS: Automated Feature Selection via Diversity-aware Interactive Reinforcement Learning](https://mlsanity.com/paper/2008.12001/) (2020)
- [Interactive Reinforcement Learning for Feature Selection with Decision Tree in the Loop](https://mlsanity.com/paper/2010.02506/) (2020)
- [Graph Soft-Contrastive Learning via Neighborhood Ranking](https://mlsanity.com/paper/2209.13964/) (2022)
- [LightCAKE: A Lightweight Framework for Context-Aware Knowledge Graph Embedding](https://mlsanity.com/paper/2102.10826/) (2021)
- [IN-Flow: Instance Normalization Flow for Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2401.16777/) (2024)
- [DEWP: Deep Expansion Learning for Wind Power Forecasting](https://mlsanity.com/paper/2401.00644/) (2024)

## Built on by (most cited first, 13 of 13)

- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)
- [TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting](https://mlsanity.com/paper/2410.04442/) (2024)
- [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)
- [ReFocus: Reinforcing Mid-Frequency and Key-Frequency Modeling for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2502.16890/) (2025)
- [Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting](https://mlsanity.com/paper/2505.11781/) (2025)
- [Robust Multivariate Time Series Forecasting against Intra- and Inter-Series Transitional Shift](https://mlsanity.com/paper/2407.13194/) (2024)
- [Rethinking Adam for Time Series Forecasting: A Simple Heuristic to Improve Optimization under Distribution Shifts](https://mlsanity.com/paper/2603.10095/) (2026)
- [SeesawNet: Towards Non-stationary Time Series Forecasting with Balanced Modeling of Common and Specific Dependencies](https://mlsanity.com/paper/2605.14551/) (2026)
- [Dynamic TMoE: A Drift-Aware Dynamic Mixture of Experts Framework for Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2605.20678/) (2026)
- [TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectra](https://mlsanity.com/paper/2609.32384/) (2026)
- [Correction-space Cross-variate Interaction for Test-time Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2609.34638/) (2026)

## Abstract (arXiv)

While most time series are non-stationary, it is inevitable for models to face the distribution shift issue in time series forecasting. Existing solutions manipulate statistical measures (usually mean and std.) to adjust time series distribution. However, these operations can be theoretically seen as the transformation towards zero frequency component of the spectrum which cannot reveal full distribution information and would further lead to information utilization bottleneck in normalization, thus hindering forecasting performance. To address this problem, we propose to utilize the whole frequency spectrum to transform time series to make full use of data distribution from the frequency perspective. We present a deep frequency derivative learning framework, DERITS, for non-stationary time series forecasting. Specifically, DERITS is built upon a novel reversible transformation, namely Frequency Derivative Transformation (FDT) that makes signals derived in the frequency domain to acquire more stationary frequency representations. Then, we propose the Order-adaptive Fourier Convolution Network to conduct adaptive frequency filtering and learning. Furthermore, we organize DERITS as a parallel-stacked architecture for the multi-order derivation and fusion for forecasting. Finally, we conduct extensive experiments on several datasets which show the consistent superiority in both time series forecasting and shift alleviation.