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）和相对最终预测误差（RFPE）提出枢轴推断方法。我们的方法基于自归一化技术，避免了经验自协方差渐近方差的估计。我们为(R)FPE提供了枢轴置信区间，发展了达到预设预测精度所需最小线性预测阶数的估计方法，并提出了关于(R)FPE超过给定阈值的（枢轴）统计检验。此外，我们还为基于过去p≥1个观测值进行线性预测得到的常用决定系数R²提供了枢轴不确定性量化，并开发了新的（枢轴）偏自相关推断工具——这些工具无需自回归过程的假设。