线性模型在时间序列预测中能有多好？

摘要

时间序列预测研究正持续转向更大型的架构——从专用Transformer到通用基础模型——其假设是模型容量决定了预测精度。我们持相反观点：通过优化预处理而非扩大模型规模，能够在极低成本下弥合大部分性能差距。我们采用岭回归作为测试平台，因其具有闭式解和可解释的权重，允许直接从搜索过程读取最优超参数。我们在八个标准基准上对上下文长度、局部归一化、正则化和数据增强进行搜索，发现了三种模式。（1）最优回溯长度具有强烈的序列特异性，且通常随预测步长呈非单调变化——拟合的幂律指数从ETTm2数据集的+0.46到Exchange和Traffic数据集的-0.19，挑战了"更长预测步长需要更长历史数据"的传统观点。（2）将归一化应用于所学到的上下文尾部比例（而非整体上下文）几乎普遍更优。（3）同一数据集内的序列对超参数偏好各异；跨序列共享的最优程度从完全共享到完全独立不等。由此得到的模型在大多数数据集-预测步长组合上超越了以往的线性预测器，并在八个基准中的六个上超过了Transformer、MLP和CNN基线。优化后的超参数还可作为数据本身的诊断工具，揭示出大型模型在训练过程中默默吸收到参数中的结构特征。

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.