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HIGHER-ORDER APPROXIMATION FOR UNCERTAINTY QUANTIFICATION IN TIME-SERIES ANALYSIS

Published online by Cambridge University Press:  22 July 2025

Annika Betken  and
Marie-Christine Düker
Annika Betken*
Affiliation:
University of Twente
Marie-Christine Düker
Affiliation:
FAU Erlangen-Nürnberg
*
Address correspondence to Annika Betken, Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands, e-mail: a.betken@utwente.nl.
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Abstract

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For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing, and uncertainty quantification admit a representation as functionals of the empirical process and therefore inherit its slow convergence. As a result, inference based on the asymptotic distribution of those quantities is significantly affected by relatively small sample sizes. We assess the quality of higher-order approximations (HOAs) of the empirical process by deriving the asymptotic distribution of the corresponding error terms. Based on the limiting distribution of the higher-order terms, we propose a novel approach to calculate confidence intervals for statistical quantities such as the median. In a simulation study, we compare coverage rates and lengths of these confidence intervals with those based on the asymptotic distribution of the empirical process and highlight some benefits of HOAs of the empirical process.

Information

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 50
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Footnotes

We thank the editor, co-editor, and referees for their careful reading of the manuscript and their thoughtful comments, which led to a significant improvement of the article. Annika Betken gratefully acknowledges financial support from the Dutch Research Council (NWO) through VENI grant 212.164. Marie-Christine Düker gratefully acknowledges financial support from the National Science Foundation under grants 1934985, 1940124, 1940276, and 2114143. This research was conducted with support from the Cornell University Center for Advanced Computing, which receives funding from Cornell University, the National Science Foundation, and members of its Partner Program.

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