# De-biased graphical Lasso for high-frequency data

## TL;DR

This paper introduces a new statistical inference framework for the precision matrix of high-frequency data, enabling accurate interval estimation and hypothesis testing in high-dimensional settings, including factor-structured data.

## Contribution

It develops an abstract asymptotic theory for the weighted graphical Lasso and its de-biased version, applicable without specifying the initial covariance estimator, and extends to factor-structured data.

## Key findings

- Established asymptotic distribution theory for de-biased graphical Lasso
- Provided methods for confidence intervals and hypothesis testing for precision matrix entries
- Extended theory to factor-structured high-frequency data

## Abstract

This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for entries of the precision matrix. To accomplish this purpose, we establish an abstract asymptotic theory for the weighted graphical Lasso and its de-biased version without specifying the form of the initial covariance estimator. We also extend the scope of the theory to the case that a known factor structure is present in the data. The developed theory is applied to the concrete situation where we can use the realized covariance matrix as the initial covariance estimator, and we obtain a feasible asymptotic distribution theory to construct (simultaneous) confidence intervals and (multiple) testing procedures for entries of the precision matrix.