Second-order asymptotic expansion for a non-synchronous covariation estimator

Arnak Dalalyan; Nakahiro Yoshida

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 3, page 748-789
  • ISSN: 0246-0203

Abstract

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In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers [Bernoulli11 (2005) 359–379, Ann. Inst. Statist. Math.60 (2008) 367–406], we derive second-order asymptotic expansions for the distribution of the Hayashi–Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order decomposition of the estimator’s distribution in the gaussian set-up, a stochastic decomposition of the estimator itself and an accurate evaluation of the Malliavin covariance. To give a concrete example, we compute the constants involved in the resulting expansions for the particular case of sampling scheme generated by two independent Poisson processes.

How to cite

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Dalalyan, Arnak, and Yoshida, Nakahiro. "Second-order asymptotic expansion for a non-synchronous covariation estimator." Annales de l'I.H.P. Probabilités et statistiques 47.3 (2011): 748-789. <http://eudml.org/doc/239624>.

@article{Dalalyan2011,
abstract = {In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers [Bernoulli11 (2005) 359–379, Ann. Inst. Statist. Math.60 (2008) 367–406], we derive second-order asymptotic expansions for the distribution of the Hayashi–Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order decomposition of the estimator’s distribution in the gaussian set-up, a stochastic decomposition of the estimator itself and an accurate evaluation of the Malliavin covariance. To give a concrete example, we compute the constants involved in the resulting expansions for the particular case of sampling scheme generated by two independent Poisson processes.},
author = {Dalalyan, Arnak, Yoshida, Nakahiro},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {edgeworth expansion; covariation estimation; diffusion process; asynchronous observations; Poisson sampling; Edgeworth expansion},
language = {eng},
number = {3},
pages = {748-789},
publisher = {Gauthier-Villars},
title = {Second-order asymptotic expansion for a non-synchronous covariation estimator},
url = {http://eudml.org/doc/239624},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Dalalyan, Arnak
AU - Yoshida, Nakahiro
TI - Second-order asymptotic expansion for a non-synchronous covariation estimator
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 3
SP - 748
EP - 789
AB - In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers [Bernoulli11 (2005) 359–379, Ann. Inst. Statist. Math.60 (2008) 367–406], we derive second-order asymptotic expansions for the distribution of the Hayashi–Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order decomposition of the estimator’s distribution in the gaussian set-up, a stochastic decomposition of the estimator itself and an accurate evaluation of the Malliavin covariance. To give a concrete example, we compute the constants involved in the resulting expansions for the particular case of sampling scheme generated by two independent Poisson processes.
LA - eng
KW - edgeworth expansion; covariation estimation; diffusion process; asynchronous observations; Poisson sampling; Edgeworth expansion
UR - http://eudml.org/doc/239624
ER -

References

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