Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting

2025-05-17

AI Summary

Existing Fourier-based and conventional wavelet-based methods struggle to model time-sensitive multi-scale patterns and are insensitive to abrupt changes in deep time series forecasting. To address these limitations, this paper proposes the Multi-Order Wavelet Derivative Transform (WDT), the first wavelet decomposition framework incorporating derivatives: it jointly leverages wavelet coefficients across successive derivative orders to jointly characterize long-term trends and abrupt changes, thereby enhancing sensitivity to variation rates and local fluctuations. Furthermore, we design WaveTS—a multi-branch architecture that enables learnable refinement of time-frequency coefficients and accurate inverse WDT reconstruction. Extensive experiments on ten benchmark datasets demonstrate that our method achieves state-of-the-art forecasting accuracy, significantly outperforming both Fourier- and conventional wavelet-based models, while maintaining high computational efficiency.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Capturing multi-scale time-sensitive patterns in forecasting
• Improving wavelet transform sensitivity to time series changes
• Enhancing forecasting accuracy with derivative-based time-frequency analysis

Innovation

• Multi-order Wavelet Derivative Transform for time-aware patterns
• Derivative-based approach magnifies rate-of-change cues
• Multi-branch WaveTS framework with inverse WDT reconstruction