PreprintCC BY-NC-ND 4.0arXiv
Self-normalization for Spectral Density Integrals
Abstract
Integrals of spectral densities are frequently used to summarize spectral characteristics of linear processes. This work studies self-normalization for estimators of such integrals based on sequential periodograms and establishes weak convergence of the corresponding processes. For linear functionals of the spectral density, self-normalization yields pivotal limiting distributions that are free of unknown spectral quantities. For non-linear functionals, however, additional components with distinct covariance structures may arise in the limiting process. We demonstrate this phenomenon for the integrated squared spectral density.
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BibTeX
@misc{dette2026selfnormalization,
title = {{Self-normalization for Spectral Density Integrals}},
author = {Holger Dette and Sebastian Kühnert},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30018},
eprint = {2608.30018},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30018},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Self-normalization for Spectral Density Integrals
AU - Holger Dette
AU - Sebastian Kühnert
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.30018
UR - https://arxiv.org/abs/2608.30018
AB - Integrals of spectral densities are frequently used to summarize spectral characteristics of linear processes. This work studies self-normalization for estimators of such integrals based on sequential periodograms and establishes weak convergence of the corresponding processes. For linear functionals of the spectral density, self-normalization yields pivotal limiting distributions that are free of unknown spectral quantities. For non-linear functionals, however, additional components with distinct covariance structures may arise in the limiting process. We demonstrate this phenomenon for the integrated squared spectral density.
ER -