線性模型在時間序列預測中能有多好？

摘要

時間序列預測研究一直穩定地朝向更大的架構發展，從專門的Transformer到通用基礎模型，其假設是模型容量才能解鎖準確度。我們採取相反的立場：大多數性能差距可透過調整預處理而非擴充模型規模，以遠更低的成本來縮小。我們以嶺迴歸作為測試平台，因為它具有封閉式解與可解釋的權重，這使得最佳超參數能直接從搜尋過程中讀取。我們針對八個標準基準數據集，搜尋上下文長度、局部正規化、正則化與資料增強，並發現三種模式。(1) 最適回溯長度具有強烈的序列特異性，且常與預測區間呈非單調關係，其擬合冪律指數範圍從ETTm2的+0.46到Exchange與Traffic的-0.19，挑戰了「較長預測區間需要更長歷史」的慣例。(2) 對上下文中的學習拖尾部分進行正規化，而非對整個上下文，幾乎是普遍偏好的做法。(3) 同一數據集中的不同序列往往對超參數有不同偏好；跨序列共享的最佳程度從完全共享到每個序列各自獨立不等。由此產生的模型在多數數據集-預測區間組合中優於先前的線性預測器，並在八個基準的六個中優於Transformer、MLP與CNN基線。這些最佳化的超參數同時可作為數據本身的診斷工具，揭示出大型模型會默默吸收到其學習參數中的結構。

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.