{"ID":2877304,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.21025","arxiv_id":"2508.21025","title":"Pivotal inference for linear predictions in stationary processes","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.","short_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 confiden...","url_abs":"https://arxiv.org/abs/2508.21025","url_pdf":"https://arxiv.org/pdf/2508.21025v5","authors":"[\"Holger Dette\",\"Sebastian Kühnert\"]","published":"2025-08-28T17:28:39Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}