High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series
Abstract
Many real-world high-dimensional time series exhibit long-memory, but Gaussian graphical model testing in this regime remains understudied. We develop a direct, data-adaptive test statistic for assessing conditional independence in the graph structure of stationary Gaussian time series. We establish a finite-sample, Berry--Esseen type Gaussian approximation bound for the statistic, which applies to both short-memory and long-memory time series. The testing procedure is fully data-adaptive using block bootstrap method, on which we provide a finite-sample validity result including in the ultra-high-dimensional scenario, and can be extended to comparing graphical structures in two-sample tests. We also develop a consistency-empowered correction to the statistic and show that such tests attain asymptotic consistency in both size and power. Our proposed method is applied to a real-world fMRI data to understand functional connectivities within brain in different periods.
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BibTeX
@misc{zhai2026highdimensional,
title = {{High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series}},
author = {Percy S. Zhai and Ping-Shou Zhong and Wei Biao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30565},
eprint = {2609.30565},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30565},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series
AU - Percy S. Zhai
AU - Ping-Shou Zhong
AU - Wei Biao Wu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30565
UR - https://arxiv.org/abs/2609.30565
AB - Many real-world high-dimensional time series exhibit long-memory, but Gaussian graphical model testing in this regime remains understudied. We develop a direct, data-adaptive test statistic for assessing conditional independence in the graph structure of stationary Gaussian time series. We establish a finite-sample, Berry--Esseen type Gaussian approximation bound for the statistic, which applies to both short-memory and long-memory time series. The testing procedure is fully data-adaptive using block bootstrap method, on which we provide a finite-sample validity result including in the ultra-high-dimensional scenario, and can be extended to comparing graphical structures in two-sample tests. We also develop a consistency-empowered correction to the statistic and show that such tests attain asymptotic consistency in both size and power. Our proposed method is applied to a real-world fMRI data to understand functional connectivities within brain in different periods.
ER -