# Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting

arXiv: https://arxiv.org/abs/2505.11781 · HTML: https://mlsanity.com/paper/2505.11781/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 68 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 30 of 45)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (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)
- [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)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [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)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [Less Is More: Fast Multivariate Time Series Forecasting with Light Sampling-oriented MLP Structures](https://mlsanity.com/paper/2207.01186/) (2022)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting](https://mlsanity.com/paper/2310.09751/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [TSLANet: Rethinking Transformers for Time Series Representation Learning](https://mlsanity.com/paper/2404.08472/) (2024)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective](https://mlsanity.com/paper/2502.10721/) (2025)
- [CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting](https://mlsanity.com/paper/2305.12095/) (2023)

## Built on by (most cited first, 4 of 4)

- [WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation](https://mlsanity.com/paper/2510.11839/) (2025)
- [RAST: A Retrieval Augmented Spatio-Temporal Framework for Traffic Prediction](https://mlsanity.com/paper/2508.16623/) (2025)
- [WaveMoE: A Wavelet-Enhanced Mixture-of-Experts Foundation Model for Time Series Forecasting](https://mlsanity.com/paper/2604.10544/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)

## Abstract (arXiv)

In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT) can capture these patterns through frequency decomposition, its coefficients are insensitive to change points in time series, leading to suboptimal modeling. To mitigate these limitations, we introduce the multi-order Wavelet Derivative Transform (WDT) grounded in the WT, enabling the extraction of time-aware patterns spanning both the overall trend and subtle fluctuations. Compared with the standard FT and WT, which model the raw series, the WDT operates on the derivative of the series, selectively magnifying rate-of-change cues and exposing abrupt regime shifts that are particularly informative for time series modeling. Practically, we embed the WDT into a multi-branch framework named WaveTS, which decomposes the input series into multi-scale time-frequency coefficients, refines them via linear layers, and reconstructs them into the time domain via the inverse WDT. Extensive experiments on ten benchmark datasets demonstrate that WaveTS achieves state-of-the-art forecasting accuracy while retaining high computational efficiency.