arXiv:2503.02609cs.LG2025-03被引 1

通过方差分析动态恢复非平稳性,提升时间序列预测精度

Lightweight Channel-wise Dynamic Fusion Model: Non-stationary Time Series Forecasting via Entropy Analysis

  • 基于方差构建通道动态融合机制,选择性恢复原始非平稳特征
  • 在7个数据集上优于现有方法,有效保留全局时序依赖关系
  • 适合处理多通道、非平稳性强的时间序列任务

真实世界时间序列具有固有的非平稳性,对预测至关重要。以往研究多采用实例归一化削弱原始序列的非平稳性以提升可预测性,但直接消除非平稳性会引发三大问题:破坏全局时序依赖、忽略通道特异性差异、导致预测过度平滑。本文理论证明方差可作为量化非平稳性的有效且可解释的代理指标。基于此,提出轻量级通道动态融合模型(CDFM),在保持归一化序列可预测性的前提下,选择性地动态恢复原始序列的内在非平稳性。首先设计双预测器模块,包含捕捉稳定模式的时间平稳预测器与建模全局动态模式的时间非平稳预测器;其次提出融合权重学习器,基于方差动态刻画不同样本的内在非平稳信息;最后引入通道选择器,通过评估非平稳性、相似性与分布一致性,有选择地从特定通道恢复非平稳信息,从而捕捉相关动态特征并避免过拟合。在七个时间序列数据集上的综合实验验证了CDFM的优越性与泛化能力。

原文摘要 · Abstract (English)

Non-stationarity is an intrinsic property of real-world time series and plays a crucial role in time series forecasting. Previous studies primarily adopt instance normalization to attenuate the non-stationarity of original series for better predictability. However, instance normalization that directly removes the inherent non-stationarity can lead to three issues: (1) disrupting global temporal dependencies, (2) ignoring channel-specific differences, and (3) producing over-smoothed predictions. To address these issues, we theoretically demonstrate that variance can be a valid and interpretable proxy for quantifying non-stationarity of time series. Based on the analysis, we propose a novel lightweight \textit{C}hannel-wise \textit{D}ynamic \textit{F}usion \textit{M}odel (\textit{CDFM}), which selectively and dynamically recovers intrinsic non-stationarity of the original series, while keeping the predictability of normalized series. First, we design a Dual-Predictor Module, which involves two branches: a Time Stationary Predictor for capturing stable patterns and a Time Non-stationary Predictor for modeling global dynamics patterns. Second, we propose a Fusion Weight Learner to dynamically characterize the intrinsic non-stationary information across different samples based on variance. Finally, we introduce a Channel Selector to selectively recover non-stationary information from specific channels by evaluating their non-stationarity, similarity, and distribution consistency, enabling the model to capture relevant dynamic features and avoid overfitting. Comprehensive experiments on seven time series datasets demonstrate the superiority and generalization capabilities of CDFM.

时间序列非平稳性动态融合通道选择

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