Edgeworth expansion for the pre-averaging estimator

TL;DR

This paper develops a second-order Edgeworth expansion for a pre-averaging estimator of quadratic variation in noisy diffusion models, enhancing the understanding of estimator distribution and enabling better confidence interval construction.

Contribution

The paper introduces a second-order Edgeworth expansion for the joint density of the estimator and its variance in noisy diffusion models, using advanced probabilistic techniques.

Findings

Derived the density expansion for the estimator and its asymptotic variance.

Provided the density expansion for the studentized statistic.

Facilitated the construction of asymptotic confidence regions.

Abstract

In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our approach is based on martingale embedding, Malliavin calculus and stable central limit theorems for continuous diffusions. Moreover, we derive the density expansion for the studentized statistic, which might be applied to construct asymptotic confidence regions.