arXiv:2606.27282cs.LG2026-06

用简单线性模型+智能预处理,就能逼近复杂模型的预测效果。

How Good Can Linear Models Be for Time-Series Forecasting?

论文配图:How Good Can Linear Models Be for Time-Series Forecasting?
图 1 · 摘自论文原文
  • 通过调优数据预处理而非扩大模型规模提升性能
  • 在8个基准上超越多数线性模型和部分深度模型
  • 揭示数据内在结构,适合想理解模型行为的研究者

时间序列预测研究趋向于使用更大架构,假设容量决定精度。本文提出相反观点:通过优化预处理而非扩展模型即可大幅缩小差距。以岭回归为测试平台,因其具有闭式解与可解释权重,能直接读取最优超参数。在8个标准基准上搜索上下文长度、局部归一化、正则化和增强策略,发现三个规律:(1)最优历史窗口长度高度依赖序列特征,且常随预测时长非单调变化,幂律指数范围从ETTm2的+0.46到Exchange与Traffic的-0.19,挑战了“更长预测需更长历史”的常规认知;(2)对历史窗口中学习到的尾部比例进行归一化,优于对整体历史归一化;(3)同一数据集内不同序列的最优超参数差异显著,跨序列共享程度从完全共享到完全独立不等。优化后的模型在多数数据集-时长组合上超越以往线性模型,在8个基准中有6个超过Transformer、MLP与CNN基线。最优超参数本身也成为诊断工具,揭示出大模型隐含吸收的数据结构。配套交互演示与代码已开源:https://sakanaai.github.io/SearchCast/。

原文摘要 · Abstract (English)

Time-series forecasting research has been moving steadily toward larger architectures, from specialized transformers to general-purpose foundation models, on the assumption that capacity is what unlocks accuracy. We take the opposite position: most of the gap can be closed at far lower cost by tuning preprocessing rather than scaling models. We use Ridge regression as the testbed, since it has a closed-form solution and interpretable weights, which let the optimal hyperparameters be read off the search directly. We search over context length, local normalization, regularization, and augmentation on eight standard benchmarks and find three patterns. (1) Optimal lookback is strongly series-specific and often non-monotonic in forecast horizon, with fitted power-law exponents ranging from $+0.46$ on ETTm2 to $-0.19$ on Exchange and Traffic, challenging the convention that longer horizons need longer history. (2) Normalizing over a learned trailing fraction of the context, rather than its entirety, is almost universally preferred. (3) Series within the same dataset often disagree on hyperparameters; the optimal degree of cross-series sharing varies from fully shared to fully per-series. The resulting models beat prior linear forecasters on most dataset-horizon entries and exceed Transformer, MLP, and CNN baselines on six of eight benchmarks. The optimized hyperparameters also serve as a diagnostic on the data itself, revealing structures that larger models absorb silently into their learned parameters. We provide an accompanying interactive online demonstration and the code at https://sakanaai.github.io/SearchCast/.

时间序列线性模型预处理可解释性

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