Edgeworth expansion for the pre-averaging estimator

被引：6

作者：

Podolskij, Mark ^{[1
]}

Veliyev, Bezirgen ^{[2
]}

Yoshida, Nakahiro ^{[3
,4
]}

机构：

[1] Aarhus Univ, Dept Math, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

[2] Aarhus Univ, Dept Econ & Business Econ, CREATES, Fuglesangs Alle 4, DK-8210 Aarhus V, Denmark

[3] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 153, Japan

[4] CREST Japan Sci & Technol Agcy, Kawaguchi, Saitama, Japan

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2017年 / 127卷 / 11期

基金：

新加坡国家研究基金会; 日本学术振兴会; 日本科学技术振兴机构;

关键词：

Diffusion processes; Edgeworth expansion; high frequency observations; quadratic variation; pre-averaging; MICROSTRUCTURE NOISE; VOLATILITY; FUNCTIONALS; JUMPS;

D O I：

10.1016/j.spa.2017.03.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：3558 / 3595

页数：38

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