# High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series

arXiv: https://arxiv.org/abs/2609.30565 · HTML: https://mlsanity.com/paper/2609.30565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Asymptotic normality and optimalities in estimation of large Gaussian graphical models](https://mlsanity.com/paper/1309.6024/) (2013)
- [Gaussian Graphical Model Estimation with False Discovery Rate Control](https://mlsanity.com/paper/1306.0976/) (2013)
- [Joint Estimation of Multiple Graphical Models from High Dimensional Time Series](https://mlsanity.com/paper/1311.0219/) (2013)
- [Confidence intervals for high-dimensional inverse covariance estimation](https://mlsanity.com/paper/1403.6752/) (2014)
- [FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting](https://mlsanity.com/paper/2003.05402/) (2020)
- [High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach](https://mlsanity.com/paper/2105.02487/) (2021)
- [Estimation of Large Covariance and Precision Matrices from Temporally Dependent Observations](https://mlsanity.com/paper/1412.5059/) (2014)
- [Simultaneous Inference for Covariance and Precision Matrices of Long-Range Dependent Time Series](https://mlsanity.com/paper/2604.16219/) (2026)
- [Goodness-of-Fit Tests for High-Dimensional Gaussian Graphical Models via Exchangeable Sampling](https://mlsanity.com/paper/2312.01815/) (2023)

## Abstract (arXiv)

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.