Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting

TL;DR

This paper introduces the WaveTS framework utilizing the multi-order Wavelet Derivative Transform to enhance deep time series forecasting by capturing multi-scale, time-sensitive patterns more effectively than traditional Fourier or Wavelet Transforms.

Contribution

The paper proposes the novel multi-order Wavelet Derivative Transform and integrates it into WaveTS, a multi-branch model that improves forecasting accuracy and efficiency.

Findings

WaveTS achieves state-of-the-art accuracy on ten benchmark datasets.

WDT enhances detection of regime shifts and subtle fluctuations.

The approach maintains high computational efficiency.

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.