泄漏积分器重构：驯服递归差分时间序列预测中的误差累积

中文摘要 AI 辅助

我们引入了泄漏积分器重构，这是一种无需训练的方法，可治愈递归差分预测中的误差累积问题。我们的第一个贡献是诊断性的：预测一步变化并通过累积求和进行积分（这是处理非平稳性的标准补救措施）实际上是一个极点在单位圆上的离散积分器，我们证明这会使非线性模型的递归展开发散，其336步误差达到表现良好的预测器的数倍（归一化MAE为1.6-3.8，而良好预测器约为0.8），在所有测试的神经架构中均如此。我们的第二个核心贡献是修复方法：通过泄漏积分器 H(z) = 1/(1 - gamma z^-1)，gamma < 1，将极点移入单位圆内，这可以证明地限制累积误差方差。在重构时应用单个固定 gamma=0.9（无需重新训练，对任何已部署的一步或基础模型预测器只需两行代码更改），它在每个预测视界都缩小误差，在七个发散架构和二十个数据集上的平均增益从 H=24 时的约3%增长到 H=96 时的23%，H=192 时的37%，以及 H=336 时的51%（在这些架构中范围为43-74%）（使用oracle极点时为78%）。至关重要的是，在没有病理情况的地方（稳定或联合预测器已达到不可约误差率），它被证明是惰性的，使其成为安全、通用的默认选择。

英文摘要

Recursive differenced forecasting, the standard remedy for non-stationarity, predicts one-step changes and integrates them by cumulative summation. We show that this reconstruction is a discrete integrator with a pole on the unit circle, so the biased increment errors of a learned nonlinear model are summed without bound and the rollout diverges: at 336 steps its normalised MAE reaches 1.6-3.8 for every neural architecture tested, against 0.80 for a stable linear recursion. We then introduce leaky-integrator reconstruction, a training-free fix that moves the pole inside the unit circle with H(z) = 1/(1 - gamma z^-1), gamma < 1, bounding the accumulation of the model's own increment errors. Applied post hoc with a single fixed gamma=0.9 (no retraining, a two-line change to any deployed one-step or foundation-model forecaster), it beats the traditional recursive integrator at every horizon, with the mean gain over seven diverging architectures and twenty datasets growing from ~3% at H=24 to 23% at H=96, 37% at H=192 and 51% at H=336 (43-75% across those architectures; 78% with an oracle pole), bringing all of them to 0.87-0.97. Based on these extensive empirical experiments, adding a leaky integrator thus improves recursive differenced time-series forecasting.

发表机构

• New York University（纽约大学）

机构由 AI 辅助整理，请以论文原文为准。