Department of Economics and Business Economics

Validity of Edgeworth expansions for realized volatility estimators

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Standard

Validity of Edgeworth expansions for realized volatility estimators. / Hounyo, Ulrich; Veliyev, Bezirgen.

In: Econometrics Journal, Vol. 19, No. 1, 2016, p. 1-32.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Harvard

APA

CBE

MLA

Vancouver

Author

Bibtex

@article{08b102d6a2b24cf0b6da8be71f71b49c,
title = "Validity of Edgeworth expansions for realized volatility estimators",
abstract = "The main contribution of this paper is to establish the formal validity of Edgeworth expansions for realized volatility estimators. First, in the context of no microstructure effects, our results rigorously justify the Edgeworth expansions for realized volatility derived in Gon{\c c}alves and Meddahi (2009, Econometrica 77, 283-306). Second, we show that the validity of the Edgeworth expansions for realized volatility might not cover the optimal two-point distribution wild bootstrap proposed by Gon{\c c}alves and Meddahi. Then, we propose a new optimal nonlattice distribution, which ensures the second-order correctness of the bootstrap. Third, in the presence of microstructure noise, based on our Edgeworth expansions, we show that the new optimal choice proposed in the absence of noise is still valid in noisy data for the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009, Bernoulli 15, 634-658). Finally, we show how confidence intervals for integrated volatility can be constructed using these Edgeworth expansions for noisy data. Our Monte Carlo simulations show that the intervals based on the Edgeworth corrections have improved the finite sample properties relatively to the conventional intervals based on the normal approximation.",
keywords = "Bootstrap, Confidence intervals, Edgeworth expansions, Pre-averaging, Realized volatility",
author = "Ulrich Hounyo and Bezirgen Veliyev",
year = "2016",
doi = "10.1111/ectj.12058",
language = "English",
volume = "19",
pages = "1--32",
journal = "Econometrics Journal",
issn = "1368-4221",
publisher = "Wiley",
number = "1",

}

RIS

TY - JOUR

T1 - Validity of Edgeworth expansions for realized volatility estimators

AU - Hounyo, Ulrich

AU - Veliyev, Bezirgen

PY - 2016

Y1 - 2016

N2 - The main contribution of this paper is to establish the formal validity of Edgeworth expansions for realized volatility estimators. First, in the context of no microstructure effects, our results rigorously justify the Edgeworth expansions for realized volatility derived in Gonçalves and Meddahi (2009, Econometrica 77, 283-306). Second, we show that the validity of the Edgeworth expansions for realized volatility might not cover the optimal two-point distribution wild bootstrap proposed by Gonçalves and Meddahi. Then, we propose a new optimal nonlattice distribution, which ensures the second-order correctness of the bootstrap. Third, in the presence of microstructure noise, based on our Edgeworth expansions, we show that the new optimal choice proposed in the absence of noise is still valid in noisy data for the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009, Bernoulli 15, 634-658). Finally, we show how confidence intervals for integrated volatility can be constructed using these Edgeworth expansions for noisy data. Our Monte Carlo simulations show that the intervals based on the Edgeworth corrections have improved the finite sample properties relatively to the conventional intervals based on the normal approximation.

AB - The main contribution of this paper is to establish the formal validity of Edgeworth expansions for realized volatility estimators. First, in the context of no microstructure effects, our results rigorously justify the Edgeworth expansions for realized volatility derived in Gonçalves and Meddahi (2009, Econometrica 77, 283-306). Second, we show that the validity of the Edgeworth expansions for realized volatility might not cover the optimal two-point distribution wild bootstrap proposed by Gonçalves and Meddahi. Then, we propose a new optimal nonlattice distribution, which ensures the second-order correctness of the bootstrap. Third, in the presence of microstructure noise, based on our Edgeworth expansions, we show that the new optimal choice proposed in the absence of noise is still valid in noisy data for the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009, Bernoulli 15, 634-658). Finally, we show how confidence intervals for integrated volatility can be constructed using these Edgeworth expansions for noisy data. Our Monte Carlo simulations show that the intervals based on the Edgeworth corrections have improved the finite sample properties relatively to the conventional intervals based on the normal approximation.

KW - Bootstrap

KW - Confidence intervals

KW - Edgeworth expansions

KW - Pre-averaging

KW - Realized volatility

UR - http://www.scopus.com/inward/record.url?scp=84965000336&partnerID=8YFLogxK

U2 - 10.1111/ectj.12058

DO - 10.1111/ectj.12058

M3 - Journal article

AN - SCOPUS:84965000336

VL - 19

SP - 1

EP - 32

JO - Econometrics Journal

JF - Econometrics Journal

SN - 1368-4221

IS - 1

ER -