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On U- and V-statistics for discontinuous Itô semimartingale

Author

Listed:
  • Mark Podolskij

    () (Aarhus University, Department of Mathematics and CREATES)

  • Christian Schmidt

    () (Aarhus University, Department of Mathematics and CREATES)

  • Mathias Vetter

    () (Christian-Albrechts-Universität zu Kiel, Mathematisches Seminar)

Abstract

In this paper we examine the asymptotic theory for U-statistics and V-statistics of discontinuous Itô semimartingales that are observed at high frequency. For different types of kernel functions we show laws of large numbers and associated stable central limit theorems. In most of the cases the limiting process will be conditionally centered Gaussian. The structure of the kernel function determines whether the jump and/or the continuous part of the semimartingale contribute to the limit.

Suggested Citation

  • Mark Podolskij & Christian Schmidt & Mathias Vetter, 2015. "On U- and V-statistics for discontinuous Itô semimartingale," CREATES Research Papers 2015-52, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2015-52
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    File URL: ftp://ftp.econ.au.dk/creates/rp/15/rp15_52.pdf
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    References listed on IDEAS

    as
    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.
    2. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
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    More about this item

    Keywords

    central limit theorems; It^o semimartingales; stable convergence; U-statistics.;

    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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