A Frequency-Domain approach to detect nonstationarity in dependent data

Mohamedou Ould Haye; Anne Philippe

A Frequency-Domain approach to detect nonstationarity in dependent data

Statistics Theory 2026-08-03 v1 Methodology

Authors: Mohamedou Ould Haye , Anne Philippe

Abstract

Distinguishing long memory behaviour from nonstationarity can be very difficult as in both cases the sample autocovariance function decays very slowly. Available stationarity tests either do not include long memory or fare poorly in terms of empirical size, especially near the boundary between long memory and nonstationarity. We propose a testing procedure based on evaluating periodograms at different epochs. Limiting distributions established here are easily tractable as sum of weighted independent $\chi^2$ random variables. Moreover, numerical studies are provided to show that the proposed approach seems to outperform existing methods.

Keywords

Mahler measure CM points conjectures L-value modular parametrization Fricke partner

Cite

@article{arxiv.2608.02253,
  title  = {A Frequency-Domain approach to detect nonstationarity in dependent data},
  author = {Mohamedou Ould Haye and Anne Philippe},
  journal= {arXiv preprint arXiv:2608.02253},
  year   = {2026}
}