Edgeworth expansion for the pre-averaging estimator

Mark Podolskij, Bezirgen Veliyev, Nakahiro Yoshida

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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.

Original languageEnglish
JournalStochastic Processes and Their Applications
Volume127
Issue11
Pages (from-to)3558-3595
Number of pages38
ISSN0304-4149
DOIs
Publication statusPublished - Nov 2017

Keywords

  • Diffusion processes
  • Edgeworth expansion
  • high frequency observations
  • pre-averaging
  • quadratic variation

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