用小波导数变换捕捉时间序列的动态变化,提升预测精度。
Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting
- 在小波变换基础上引入导数,增强对变化点的敏感性。
- 在10个基准数据集上达到领先性能,计算效率高。
- 适合需要捕捉突变和细微波动的时序预测任务。
在深度时间序列预测中,傅里叶变换(FT)被广泛用于频率表征学习,但难以捕捉多尺度、时敏模式。尽管小波变换(WT)可通过频率分解捕获这些模式,其系数对时间序列中的突变点不敏感,导致建模效果不佳。为此,我们提出基于小波变换的多阶小波导数变换(WDT),能够提取涵盖整体趋势与微小波动的时间感知模式。与直接建模原始序列的标准FT和WT不同,WDT作用于序列的导数,选择性放大变化率信号,揭示对时序建模尤为关键的突发状态转移。实际应用中,我们将WDT嵌入名为WaveTS的多分支框架,该框架将输入序列分解为多尺度时频系数,通过线性层优化,并利用逆WDT重构回时域。在10个基准数据集上的大量实验表明,WaveTS不仅达到当前最优预测精度,还保持了较高的计算效率。
原文摘要 · Abstract (English)
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.
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