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）发展了枢轴推断方法。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提供了枢轴置信区间，建立了为达到预定预测精度所需线性预测最小阶数的估计量，并提出了(R)FPE超过给定阈值的假设的（枢轴）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$R^2$提供了枢轴不确定性量化，并为偏自相关函数发展了新的（枢轴）推断工具，这些工具无需自回归过程的假设。