在准确性与及时性前沿上的预测：两种新的‘前瞻’预测器
Forecasting on the Accuracy-Timeliness Frontier: Two Novel `Look Ahead' Predictors
AI总结：
本文提出两种新的‘前瞻’预测方法，通过整合准确性与及时性的权衡，揭示了预测的完整有效前沿，超越了传统MSE方法的局限。
摘要：
我们重新审视传统的均方误差（MSE）预测范式，通过正式整合准确性与及时性之间的权衡：准确性由MSE（或目标相关性）定义，及时性由进步（或相位过剩）定义。虽然MSE优化的预测器在跟踪水平方面是准确的，但它们牺牲了动态领先，导致它们落后于变化的目标。为了解决这个问题，我们引入了两种‘前瞻’框架——解耦于现在（DFP）和峰值相关性转移（PCS），并为它们的优化提供闭式解。值得注意的是，经典的MSE预测器被证明是在这些框架中的特殊情况。此外，我们的方法在任何给定的准确性水平下实现最大进步，因此我们的方法揭示了准确性与及时性权衡的完整有效前沿，而MSE仅代表一个点。我们还推导了一个通用上界，该上界在一致性约束下为任何线性预测器的领先度提供上限，并证明我们的方法达到这个上限。我们通过在预测和实时信号提取中的应用验证了这种方法，引入了领先指标标准和定制的线性基准。
英文摘要：
We re-examine the traditional Mean-Squared Error (MSE) forecasting paradigm by formally integrating an accuracy-timeliness trade-off: accuracy is defined by MSE (or target correlation) and timeliness by advancement (or phase excess). While MSE-optimized predictors are accurate in tracking levels, they sacrifice dynamic lead, causing them to lag behind changing targets. To address this, we introduce two `look-ahead' frameworks--Decoupling-from-Present (DFP) and Peak-Correlation-Shifting (PCS)--and provide closed-form solutions for their optimization. Notably, the classical MSE predictor is shown to be a special case within these frameworks. Dually, our methods achieve maximum advancement for any given accuracy level, so our approach reveals the complete efficient frontier of the accuracy-timeliness trade-off, whereas MSE represents only a single point. We also derive a universal upper bound on lead over MSE for any linear predictor under a consistency constraint and prove that our methods hit this ceiling. We validate this approach through applications in forecasting and real-time signal extraction, introducing a leading-indicator criterion and tailored linear benchmarks.
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