Pivotal inference for linear predictions in stationary processes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914474699522048 |
|---|---|
| author | Dette, Holger Kühnert, Sebastian |
| author_facet | Dette, Holger Kühnert, Sebastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pivotal inference for linear predictions in stationary processes Dette, Holger Kühnert, Sebastian Statistics Theory Methodology 62M10, 62M20 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. |
| title | Pivotal inference for linear predictions in stationary processes |
| topic | Statistics Theory Methodology 62M10, 62M20 |
| url | https://arxiv.org/abs/2508.21025 |