Aarhus University Seal

On U- and V-statistics for discontinuous Ito semimartingales

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


  • Mark Podolskij
  • Christian Schmidt, Denmark
  • Mathias Vetter, Kiel University, Germany

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.

Original languageEnglish
JournalAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
Pages (from-to)1007-1050
Number of pages44
Publication statusPublished - 2017

    Research areas

  • High frequency data, Limit theorems, Semimartingales, Stable convergence, U-statistics

See relations at Aarhus University Citationformats

ID: 96769943