In this paper we develop pivotal inference for the final (FPE) and relative final prediction error (RFPE) of linear forecasts in stationary processes. Our approach is based on a self-normalizing technique and avoids the estimation of the asymptotic variances of the empirical autocovariances. We provide pivotal confidence intervals for the (R)FPE, develop estimates for the minimal order of a linear prediction that is required to obtain a prespecified forecasting accuracy and also propose (pivotal) statistical tests for the hypotheses that the (R)FPE exceeds a given threshold. Additionally, we provide pivotal uncertainty quantification for the commonly used coefficient of determination $R^2$ obtained from a linear prediction based on the past $p \geq 1$ observations and develop new (pivotal) inference tools for the partial autocorrelation, which do not require the assumption of an autoregressive process.

翻译：本文针对平稳过程中线性预测的最终预测误差（FPE）与相对最终预测误差（RFPE）发展了关键推断方法。我们的方法基于自标准化技术，避免了经验自协方差渐近方差的估计。我们为（R）FPE提供了关键置信区间，发展了为达到预设预测精度所需线性预测最小阶数的估计方法，并针对（R）FPE超过给定阈值的假设提出了（关键）统计检验。此外，我们为基于过去 $p \geq 1$ 个观测值的线性预测中常用的决定系数 $R^2$ 提供了关键不确定性量化，并为偏自相关函数发展了新的（关键）推断工具，这些工具无需自回归过程的假设。