Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting
This work addresses a key limitation in time series forecasting for applications requiring precise pattern detection, though it appears incremental as it builds on existing wavelet transforms.
The paper tackles the problem of capturing multi-scale, time-sensitive patterns in deep time series forecasting by introducing the multi-order Wavelet Derivative Transform (WDT), which extracts time-aware patterns from derivatives to improve modeling of abrupt changes. Experiments on ten benchmark datasets show that WaveTS, a framework embedding WDT, achieves state-of-the-art forecasting accuracy with high computational efficiency.
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.