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Edgeworth expansion for functionals of continuous diffusion processes

Author

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  • Mark Podolskij

    () (Heidelberg University and CREATES)

  • Nakahiro Yoshida

    () (Graduate School of Mathematical Science)

Abstract

This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations.

Suggested Citation

  • Mark Podolskij & Nakahiro Yoshida, 2013. "Edgeworth expansion for functionals of continuous diffusion processes," CREATES Research Papers 2013-33, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2013-33
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    File URL: ftp://ftp.econ.au.dk/creates/rp/13/rp13_33.pdf
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    References listed on IDEAS

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    1. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
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    Cited by:

    1. Mark Podolskij & Bezirgen Veliyev & Nakahiro Yoshida, 2015. "Edgeworth expansion for the pre-averaging estimator," Papers 1512.04716, arXiv.org.

    More about this item

    Keywords

    diffusion processes; Edgeworth expansion; high frequency observations; power variation.;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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