[TRR 391] 2025-11-28 | Sebastian Kühnert | Pivotal inference for predictions in stationary processes

This is the presentation "Pivotal inference for linear predictions in stationary processes" from Sebastian Kühnert given as part of the TC02 workshop “Spatio-temporal Statistics in High Dimensions,” held from November 27 to 28, 2025, at TU Dortmund University. The workshop offered a rich program with invited and contributed talks covering cutting-edge topics such as high-dimensional regularization, spatio-temporal covariance estimation, distribution- and copula-based forecasting, VAR and cointegration models, and probabilistic modelling for energy, climate and beyond. 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 novel 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 new (pivotal) inference tools for the partial autocorrelation, which do not require the assump-tion of an autoregressive process. TRR 391 is a Collaborative Research Center/Transregio funded by the DFG (Deutsche Forschungsgemeinschaft). It is about to establish an internationally leading research center in the Ruhr Area for the development of statistical methodology that can process all types of spatio-temporal data from energy production and distribution, as well as transport of people and goods. In TRR 391, we model, estimate, and predict spatio-temporal processes occurring in economic and technical applications. In doing so, we exploit the formal similarity of relevant statistical problems for methodological synergies and develop key techniques for the analysis of spatio-temporal data, which will enable efficient data-based decision-making in various areas of implementing the energy and transport transition over the next decades.