AUTHOR=Danioko Sidy , Zheng Jianwei , Anderson Kyle , Barrett Alexander , Rakovski Cyril S. 

TITLE=A Novel Correction for the Adjusted Box-Pierce Test

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=8

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.873746

DOI=10.3389/fams.2022.873746

ISSN=2297-4687

ABSTRACT=<p>The classical Box-Pierce and Ljung-Box tests for auto-correlation of residuals possess severe deviations from nominal type I error rates. Previous studies have attempted to address this issue by either revising existing tests or designing new techniques. The Adjusted Box-Pierce achieves the best results with respect to attaining type I error rates closer to nominal values. This research paper proposes a further correction to the adjusted Box-Pierce test that possesses near perfect type I error rates. The approach is based on an inflation of the rejection region for all sample sizes and lags calculated <italic>via</italic> a linear model applied to simulated data that encompasses a large range of data scenarios. Our results show that the new approach possesses the best type I error rates of all goodness-of-fit time series statistics.</p>