Higher-order approximation for uncertainty quantification in time-series analysis
Betken A, Düker MC (2025)
Publication Type: Journal article
Publication year: 2025
Journal
DOI: 10.1017/S0266466625100054
Abstract
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.
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APA:
Betken, A., & Düker, M.-C. (2025). Higher-order approximation for uncertainty quantification in time-series analysis. Econometric Theory. https://doi.org/10.1017/S0266466625100054
MLA:
Betken, Annika, and Marie-Christine Düker. "Higher-order approximation for uncertainty quantification in time-series analysis." Econometric Theory (2025).
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