Title: Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Time Series Forecasting, Deep Learning, Wavelet Transform, Frequency Derivative Learning

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 abrupt changes in the 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, 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 multiple benchmark datasets demonstrate that WaveTS achieves state-of-the-art forecasting accuracy while retaining high computational efficiency.

TL;DR: This paper proposes WaveTS, a multi-branch model that applies a multi-order Wavelet Derivative Transform to highlight both trends and abrupt changes, delivering state-of-the-art forecasting accuracy with high efficiency on ten benchmark datasets.