# Pivotal inference for linear predictions in stationary processes

## TL;DR

This paper introduces pivotal inference methods for linear prediction errors in stationary processes, providing confidence intervals, hypothesis tests, and uncertainty quantification without estimating asymptotic variances.

## Contribution

It develops self-normalizing, pivotal inference techniques for prediction errors, partial autocorrelation, and R-squared in stationary processes, avoiding variance estimation.

## Key findings

- Pivotal confidence intervals for (R)FPE are constructed.
- Estimates for minimal model order for desired accuracy are provided.
- New inference tools for partial autocorrelation without AR assumptions are developed.

## Abstract

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.

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Source: https://tomesphere.com/paper/2508.21025